Milwaukee or New York?

Neither city is a beach destination, but New York has the better swimming. Milwaukee's sand faces Lake Michigan, where Bradford Beach is good for volleyball and lounging, but the fresh water stays cool and an offshore wind can chill it overnight, so many people only paddle.

New York has real Atlantic surf at the end of the subway: Coney Island with its boardwalk and rides, and the longer, emptier Rockaways where people surf. The sea warms enough for proper swimming in midsummer, though it comes with big weekend crowds.

Milwaukee eats like the Upper Midwest, and that is its charm: the Friday fish fry with potato pancakes, frozen custard, cheese curds, a supper club with a relish tray, and taprooms in Walker's Point. It is hearty, cheap and distinctive, but the range is narrow and the fine-dining tier is small.

New York is on another level entirely. You can eat Fujianese in Flushing, Tibetan in Jackson Heights and Italian on Arthur Avenue, and then book one of the world's great tasting menus. Even its everyday staples, the slice, the bagel and the deli pastrami, are reasons to come.

Milwaukee has one memorable building, Calatrava's winged art museum on the lake, plus the Harley-Davidson Museum and the brewing-era mansions and Polish basilica that tell its immigrant story. Together they make a satisfying couple of days.

New York's museums alone outweigh that many times over: the Met, MoMA, the Guggenheim, Natural History and the Cloisters. Then come the landmarks everyone knows, from the Statue of Liberty and Ellis Island to Grand Central and the Brooklyn Bridge. A culture-led trip could go on for a week or more.

Milwaukee's night out is the corner tavern: old brewery signs, a pool table and regulars at the bar, with summer beer gardens and game-night crowds by the stadium. There is little clubbing, and last orders come at around 2am.

New York doesn't close at all. You can move from a Lower East Side speakeasy to a West Village wine bar to a warehouse party in Bushwick that runs past dawn, with late trains to get you home. No night out in Milwaukee comes close to that range or those hours.

The two are broadly level outdoors, but the settings are different. Milwaukee has an open horizon: Lake Michigan looks like the sea from Olmsted's Lake Park bluffs, long flat trails follow the shore, and the glacial hills and lakes of Kettle Moraine lie about an hour inland.

New York's green space is designed parkland, with Central Park (also an Olmsted landscape), Prospect Park and the High Line. The wilder country is steeper, though. A train up the Hudson reaches the rocky climbs of Breakneck Ridge, which offer more of a challenge than anything near Milwaukee.

Each city has a bigger neighbour about an hour and a half away by train: Chicago from Milwaukee, Philadelphia from New York. Beyond that, Milwaukee offers a short, pleasant list of Madison, Cedarburg's stone mills, Frank Lloyd Wright in Racine and the gardens of Kohler, with farmland beyond.

New York has more to choose from. Princeton and New Haven are in one direction, and up the Hudson there are Gilded Age estates, Dia Beacon and the sculpture fields of Storm King, so it can fill more days out without needing a car.

New York has more for children, with the dinosaur halls at Natural History, the Bronx Zoo, the aquarium beside Coney Island's rides and the free Staten Island Ferry. The catch is the stairs-only subway stations with a pushchair, small hotel rooms and Midtown crowds.

Milwaukee offers less but is much easier. Its zoo, Discovery World's aquariums and the Mitchell Park Domes are a short, easy drive apart, parking is simple and the pace is gentle. Come in summer, because the winter cold keeps families indoors.

In New York a car is a burden. The Manhattan grid is easy to walk, and the subway runs all night across four boroughs, with ferries and Citi Bike filling the gaps, though the express lines and weekend reroutes take some learning.

Milwaukee's walkable part is small: downtown, the Third Ward and the Riverwalk, plus a short streetcar line. To reach the zoo, the Harley-Davidson Museum or Kettle Moraine, most visitors drive or call a ride.

This is one of the widest gaps between the two. Milwaukee's shopping comes down to a few Third Ward boutiques, vintage and records on Brady Street and Wisconsin cheese at the Public Market, and for big brands the locals drive to suburban malls.

New York runs from Bergdorf Goodman and the Fifth Avenue flagships through SoHo's labels to Brooklyn's young designers, rare-book dealers and weekend flea markets. For many visitors the shopping is reason enough to go.

Milwaukee is clearly the cheaper trip. Rooms cost well below coastal rates, a beer in a neighbourhood tavern is cheap and the lakefront festivals cost little, though tax, tipping and a hire car still add up, as anywhere in the United States.

New York is among the most expensive cities anywhere, especially for Manhattan hotels, cocktails and theatre seats. Slices, Queens restaurants, the flat subway fare and free parks help, and staying in Brooklyn or Queens cuts the room bill.

Milwaukee does well for its size, with a symphony, an opera company, a ballet and the ornate 1895 Pabst Theater, and in summer it has Summerfest, with hundreds of acts on the lakefront. For the rest of the year the programme is good but local.

New York has the most of anywhere: Broadway, the Met Opera and the Philharmonic at Lincoln Center, Carnegie Hall, Village jazz clubs, Harlem gospel and free Shakespeare in the park. A culture lover can see something world-class every night of the trip.

Neither city is a spa destination, but New York has the more interesting bathing. There is a bathhouse in the East Village dating from the 1800s, Russian banyas in Brighton Beach and big Korean-style spas nearby in Queens and New Jersey, though the noise of the city works against real rest.

Milwaukee has the calmer pace, but beyond hotel spas there is nothing to bathe in, and a proper spa day means a drive to Kohler. Its gentlest pleasure is a slow walk by the lake.