New York City is the city against which all other cities measure themselves — the standard of urban ambition, cultural production, financial power and human density that has set the benchmark since the 1920s and shows no signs of relinquishing it. With 8.3 million people in five boroughs and 20 million in the metropolitan area, it is the most populous city in the United States and the most visited in the world, receiving 66 million tourists annually. The specific quality that distinguishes New York from other great cities is its absolute democratic commitment to excellence: the finest museums, the greatest restaurants, the most innovative theatre, the most ambitious architecture are all available to anyone prepared to walk to them. In a city where 800 languages are spoken, the only real requirement is curiosity.

The grid plan of Manhattan — imposed by the Commissioners' Plan of 1811, which divided the island into numbered streets and avenues before most of them existed — is the most legible street system in any major world city, and it gives Manhattan the specific pleasure of always knowing where you are and how far you are from where you need to be. The island's neighbourhoods are defined by their relationship to this grid: Greenwich Village (where the grid breaks into irregular blocks, a reminder of the pre-grid street pattern underneath); Midtown (the canyon of skyscrapers where the grid is most visually overwhelming, especially on a clear December morning when the sun tracks directly down 42nd Street at the solstice — the Manhattanhenge effect); Harlem (where the grid meets the brownstone culture of the 19th century and the jazz history of the 20th).

The Metropolitan Museum of Art — occupying 2 million square feet of Central Park's eastern edge — is the greatest encyclopaedic art museum on earth: Egyptian antiquities, Greek and Roman sculpture, European Old Masters, American painting, arms and armour, musical instruments, fashion, Asian art, all in permanent collection of 1.5 million objects with the Impressionist collection alone worth an international trip. The MoMA in Midtown, the Guggenheim in Frank Lloyd Wright's spiral on 5th Avenue, and the Whitney in its Renzo Piano building at the High Line terminus complete the most concentrated museum quarter in the world, all within 2 miles of each other.

Los Angeles is the most misrepresented city in America — not because the clichés are wrong (the freeways, the sunshine, the pursuit of beauty and fame) but because they are so selective. The city of 4 million people spread across 503 square miles is also the most diverse city in the United States by national origin, the city with the largest Mexican-American population outside Mexico, the city that has produced the dominant global cultural products of the 20th and 21st centuries (film, recorded music, television), and a city of extraordinary geographical setting: mountains on three sides, ocean on the fourth, with the Santa Monica Mountains running through its centre like a spine of chaparral and coyotes.

Hollywood — the neighbourhood rather than the industry, though they occupy the same geography — is the starting point for understanding what LA is, and also, paradoxically, what it is not: the production studios moved to Burbank and Culver City decades ago, the actual film lots are industrial parks behind security fences, and the Hollywood Boulevard tourist walk bears approximately the same relationship to the film industry as a souvenir shop bears to the artwork it reproduces. The actual industry is everywhere and nowhere: in the coffee shops of Silver Lake where screenwriters work, in the recording studios of North Hollywood, in the post-production facilities of Santa Monica, in the agents' offices of Beverly Hills. The Getty Center — Richard Meier's 1997 hilltop campus above the 405, with its gardens, its extraordinary collections of European art and its view from Santa Monica to downtown — is the most complete single expression of LA's specific combination of wealth, aesthetic ambition and environmental grandeur.

The food culture of Los Angeles has become, since approximately 2010, the most interesting in America: not because of its Michelin-starred restaurants (though those exist) but because of the extraordinary concentration of immigrant food cultures from Mexico, El Salvador, Korea, Japan, Vietnam, Ethiopia, Armenia, Iran and forty other countries, all operating at the level of authenticity that only a large immigrant population making food for itself (not for tourists) can achieve. Koreatown's 24-hour barbecue restaurants, the San Gabriel Valley's Cantonese and Sichuan restaurants, the Boyle Heights taco trucks at midnight — the best food in Los Angeles is consistently the cheapest food in Los Angeles, and consistently the least represented in any food guide.

Chicago is the city that invented American urban architecture and has never stopped. The Great Fire of 1871 that destroyed the original city created, paradoxically, the greatest opportunity in the history of modern urban design: an entire city to rebuild simultaneously, with new technology (the steel frame), new ambition, and new money. The results — the Chicago School of architecture, the invention of the skyscraper, the modern grid city, the urban park system — fundamentally changed how cities are built everywhere in the world. Every large city on earth is descended, architecturally, from the decisions made in Chicago between 1872 and 1900.

The Loop — Chicago's central business district, named for the elevated railway that runs a circuit around its edges since 1897 — contains the most concentrated display of 20th-century American architecture in the world: the Rookery (Burnham and Root, 1888), the Auditorium Theatre (Adler and Sullivan, 1889), the Chicago Cultural Center (originally the city library, 1897, with its extraordinary Tiffany glass domes), the Willis Tower (Skidmore, Owings and Merrill, 1973 — still the tallest building in the Western Hemisphere for 25 years after its completion), and the Millennium Park with Anish Kapoor's Cloud Gate (2006) — the reflective steel bean that has become the city's emblem and that continues to astonish in every light and weather condition. Along the lakefront, the Museum Campus groups three world-class institutions — the Art Institute of Chicago (the finest collection of Impressionist and Post-Impressionist art in North America), the Field Museum of Natural History, and the Shedd Aquarium — within a ten-minute walk of each other on a spectacular lakeside site.

Chicago's food culture has always been democratic and carnivorous: the Chicago deep dish pizza (a thick-crust pie with the cheese beneath the sauce, invented at Pizzeria Uno in 1943 and still served there on East Ohio Street), the Chicago-style hot dog (never with ketchup, always with mustard, relish, onion, tomato, pickle and sport peppers on a poppy seed bun — a complete meal in a single portable object), and the specific culture of the Chicago steakhouse (Gibsons, Gene and Georgetti, Chicago Cut — all operating on the principle that the beef should be the best available and the sides should not compete with it) define a food culture that is as self-confident and as entirely itself as the architecture.

San Francisco occupies a peninsula of 49 square miles between the Pacific Ocean and the San Francisco Bay, and the combination of its small geographic footprint, extraordinary topography (the 43 hills, the Bay, the fog that rolls in through the Golden Gate each afternoon in summer) and the specific human history that has unfolded on it — the Gold Rush, the earthquake of 1906, the Beat Generation of the 1950s, the Summer of Love of 1967, the AIDS crisis and the activist response that shaped modern queer culture, the first dot-com boom, the current technology industry that has made its concentration of billionaires the highest per capita of any city in the world — gives it a density of identity that cities ten times its size rarely achieve.

The Golden Gate Bridge (1937, Joseph Strauss chief engineer, Russ Cone colour consultant — the specific International Orange was his choice, against the Navy's preference for grey) is the most beautiful engineered structure in North America: 2.7 kilometres of suspension bridge between two Art Deco towers at the entrance to the Bay, painted a colour that makes it simultaneously visible in fog and incandescent in sunshine. The view from the Marin Headlands on the north side of the bridge, looking back at the bridge and the city, is the finest single urban panorama in the United States. The Ferry Building on the Embarcadero — a Beaux Arts landmark from 1898, now housing an exceptional food market that opens Tuesday, Thursday and Saturday — is the best single address for the specific culture of the Bay Area's extraordinary agricultural hinterland: Dungeness crab from the Bay, Hog Island oysters from Tomales Bay, dry-farmed tomatoes from Marin County, artisan cheese from Cowgirl Creamery, sourdough from Tartine.

The Mission District — San Francisco's historically Latino neighbourhood, now the most gastronomically interesting in the city — contains the best burritos in the world (the Mission burrito, a specific format of large foil-wrapped cylinder containing rice, beans, meat, salsa and sour cream, invented here in the 1960s) and some of the finest restaurants in the Bay Area, operating in former auto-repair shops and converted industrial spaces with the specific DIY ambition that San Francisco does better than anywhere else in the country. The Dolores Park panorama — looking down the hill over the city and the Bay, Castro District in the foreground, downtown behind — is the definitive San Francisco photograph that no tourist guide will ever stop using.

Miami is the only major American city with a genuinely bilingual culture — a city where Spanish and English coexist with equal civic status, where the radio stations, restaurants, business conversations and street signs reflect a population that is 70% Hispanic or Latino and predominantly of Cuban, Venezuelan, Colombian, Dominican and Brazilian origin. The specific culture that has emerged from this combination — the Miami Sound that produced Gloria Estefan, Marc Anthony, Pitbull and Bad Bunny; the art fair culture of Art Basel Miami Beach (December, the most important art market event in the Western Hemisphere); the architectural culture of the South Beach Art Deco district — is completely unlike any other American city and entirely unlike any Latin American city. Miami is its own thing.

The South Beach Art Deco Historic District — a 1.5-square-mile concentration of some 800 Art Deco buildings from the 1920s to the 1940s, painted in the pastel colours that the Miami Design Preservation League campaigned to restore in the 1970s — is the most complete surviving Art Deco urban district in the world. Ocean Drive, Collins Avenue, Washington Avenue: the architects (Henry Hohauser, L. Murray Dixon, Albert Anis) were working at speed in a boom town, producing buildings of real quality that combined Streamline Moderne efficiency with a tropical exuberance of terrazzo, neon and porthole windows that has no equivalent in Miami's putative European sources. The Fontainebleau Hotel (1954, Morris Lapidus) is the summit of this tradition: a building designed to make every guest feel like a movie star, with the curved pool deck, the waterfall wall and the specific excess that makes Miami the city where American prosperity has always come to be most fully itself.

Wynwood — the former warehouse district north of Downtown, now the most concentrated open-air street art district in the world — was transformed beginning in 2009 by the Wynwood Walls project, which commissioned muralists from around the world to cover entire building facades. The district now contains galleries, restaurants, and boutiques alongside the murals, and the Pérez Art Museum Miami (Herzog & de Meuron, 2013) and the Institute of Contemporary Art complete an arts quarter that attracts international collectors and makes Miami a serious player in the contemporary art world for eleven months of the year and the most important player of all in December during Art Basel.

Washington D.C. is the only major world capital designed entirely from scratch on a blank site, and the L'Enfant Plan of 1791 — the Baroque diagonal avenues overlaid on a grid, the monumental ceremonial axis from the Capitol to the Lincoln Memorial, the system of squares and circles named after states and heroes — is still legible in the modern city as the founding intention. The city was built to represent the ambitions of a new republic, and it does, in the Mall's alignment of democratic monuments and the Capitol dome that Thomas Crawford designed to be visible from every approaching road.

The National Mall — a 3-kilometre grassed promenade from the Capitol to the Lincoln Memorial, flanked by the Smithsonian museums and punctuated by the Washington Monument (the tallest obelisk in the world at 169 metres) and the World War II, Korea and Vietnam memorials — is the most symbolically concentrated public space in America. The Vietnam Veterans Memorial (Maya Lin, 1982) is the most affecting war memorial in the world: a V-shaped black granite wall inscribed with the names of 58,318 Americans killed, positioned so that the visitor's reflection overlaps the names, making the act of reading it simultaneously intimate and public. The Lincoln Memorial (Henry Bacon, 1922), with Daniel Chester French's colossal seated Lincoln, is the most rhetorically powerful architectural statement in Washington — the site of Marian Anderson's 1939 concert, of Martin Luther King's 1963 "I Have a Dream" speech, of every major American public statement about the meaning of the republic.

The Smithsonian Institution — 19 museums and galleries, all free to enter, all on or near the Mall — is the most remarkable public cultural institution in the world. The National Air and Space Museum contains the Wright Flyer, Charles Lindbergh's Spirit of St Louis, Neil Armstrong's Apollo 11 command module and John Glenn's Mercury Friendship 7 capsule. The National Museum of American History contains Julia Child's kitchen, a Star-Spangled Banner from the War of 1812, and a complete survey of American cultural and technological history. The National Gallery of Art contains the only Leonardo in the Western Hemisphere. And all of it is free, funded by federal tax, belonging to every American and available to every visitor.

Boston is the most European city in America — a walkable, historically dense, intellectually serious city that has been continuously inhabited since 1630 and shows it in every block of the original peninsula, where the pre-grid street pattern of colonial lanes and market squares survives beneath the 19th-century development. It is also the most academic city in America: the Boston metropolitan area contains 35 colleges and universities, including Harvard (the oldest in America, founded 1636) and MIT (the most influential science and engineering institution in the world), and the culture of the city — its bookshops, its conversations, its restaurants, its politics — is permanently inflected by the presence of 250,000 students.

The Freedom Trail — the 4km red-brick path connecting 16 sites of American Revolutionary history, from Boston Common (where British troops camped in 1775) to Bunker Hill (where the first major battle of the Revolution was fought) — is the most coherent historical walking tour in any American city, and it works because the sites are not reconstructions but the actual buildings: the Paul Revere House (1680, the oldest surviving building in downtown Boston, where Revere lived when he made his midnight ride in 1775), the Old North Church (1723, from whose steeple two lanterns were hung as the signal that the British were crossing the Charles River), the Faneuil Hall (1742, the meeting house where the revolutionaries argued their case). This is American history at full resolution.

The North End — Boston's Italian neighbourhood, the oldest continuously inhabited neighbourhood in America, still with its own Catholicism, its own politics and its own bakeries — is the best place in the city to eat: cannoli at Mike's Pastry (since 1946), ricotta gnocchi at any of the dozen family-run trattorias on Hanover Street, clam chowder in the specific New England style (cream, not tomato) that is the defining dish of the Massachusetts coast. The Boston Public Garden, adjacent to the Common, has the Swan Boats (pedal-powered boats shaped as swans, operating since 1877) and, in October, the most extraordinary urban display of autumn colour — maples, oaks, ginkgos all turning simultaneously in the climate of New England.

Las Vegas is the most honest city in America — the only city in the country that is exactly what it says it is, without pretension and without apology. It was built in the Nevada desert in the 1940s specifically to do one thing (separate gamblers from their money as pleasurably as possible) and it has pursued this mission with a consistency of purpose, an escalation of scale and an architectural ambition that has produced, over eighty years, the most extraordinary concentration of themed built environments on earth. The Strip — the section of Las Vegas Boulevard South that runs from Mandalay Bay to the Stratosphere — is one of the most remarkable streetscapes in the world: not because any individual building is architecturally significant, but because the collective effect of the casinos, hotels, fountains, neon signs and human traffic at 2am creates an environment with no precedent in the history of urban design.

The great casino hotels are each a complete themed world: The Venetian (Grand Canal, gondolas, Doge's Palace replica — a Venice that is simultaneously more ludicrous and more structurally coherent than the original); Caesar's Palace (Roman imperial architecture from 1966, now so thoroughly absorbed into American cultural mythology that its neoclassical columns and goddesses feel more Roman than Rome); the Bellagio (the most operatically serious of the Strip hotels, with its 8-acre lake and the dancing fountain show choreographed to music that is genuinely moving at night); and the MSG Sphere (2023, James Dolan, the largest spherical structure in the world — a 112-metre dome whose entire exterior surface is a programmable LED screen visible from across the desert). The architecture of Las Vegas is the architecture of pure spectacle, and it is the most serious commitment to spectacle as an architectural programme that has ever been attempted.

The Grand Canyon is 4 hours from Las Vegas by car (via the South Rim). Zion National Park is 2.5 hours. Bryce Canyon is 4 hours. The Valley of Fire State Park is 1 hour. Las Vegas is uniquely positioned as the gateway to the most extraordinary concentration of desert landscape in North America, and the combination of the Strip at midnight and the Zion Narrows hike at 7am the following morning is one of the most complete contrasts of American experience available in a single 24-hour period.

Seattle is the American city where the outdoors and the indoors are least separated: a city of mountains, water, forests and volcanoes that happens to contain also the global headquarters of Amazon, Boeing, Microsoft (in the suburbs), Starbucks and Alaska Airlines, and a music scene that produced Jimi Hendrix, Heart, Soundgarden, Nirvana, Pearl Jam and Death Cab for Cutie. The specific quality of Pacific Northwest urbanism — the grey drizzle that functions as social lubricant (everyone goes inside together), the coffee culture that is the most serious in America, the relationship with the wilderness that begins at the city's edges and extends, uninterrupted, to the Canadian border — is unlike anything else in the country.

Pike Place Market (1907, the oldest continuously operated public farmers' market in the United States) is the best single address in Seattle: fish being thrown across stalls by fishmongers who have made the throw-and-catch a performance since the 1980s, the first Starbucks (1971, still operating in the original Pike Place location with the original brown logo, always with a queue), the flower market, the cheese vendors, the buskers, and the Post Alley entrance where the Gum Wall — a stretch of wall entirely covered in chewing gum since the 1990s, an accidental art installation of genuine repulsiveness and undeniable presence — attracts photographers. The Pike-Pine corridor in Capitol Hill, adjacent to the market district, contains the best restaurant and bar scene in Seattle, dense with the specific Pacific Northwest aesthetic of reclaimed wood, exposed concrete and craft beer menus of extraordinary ambition.

The Space Needle (1962, John Graham for the Seattle World's Fair) is the most graceful piece of Googie architecture in America: a flying saucer on a tripod, 184 metres high, with a revolving restaurant and an observation deck that on clear days shows Mount Rainier to the south (14,411 feet, the most topographically prominent mountain in the contiguous United States), the Olympic Mountains to the west, the Cascades to the east, and the entire Puget Sound archipelago below. The combination of volcano, ocean, forest and city visible simultaneously from the Needle is available in no other American city — and it is the view that most completely explains why people move to Seattle and then never leave.