Denver or Minneapolis?

Neither city has a coast, but Minneapolis puts swimming in the middle of town. Lake Harriet, Bde Maka Ska and Lake Nokomis have sandy strips with lifeguards in summer, so an evening swim after sightseeing is easy from late June to early September.

In Denver the swimming is out on the edge of the city, at the reservoir beaches of Cherry Creek and Chatfield, and the mountain lakes stay cold. A hotel or public pool is the realistic way to cool off.

Both cities eat better than their reputations suggest, and both are serious beer towns, with taprooms in old warehouses in RiNo and Northeast alike. The difference is in what you go looking for. Denver's flavour is Southwestern: green chile, breakfast burritos, bison and lamb, plus Vietnamese and Mexican cooking along Federal Boulevard.

Minneapolis draws more widely on its immigrant communities, with Somali, Ethiopian, Hmong and Mexican kitchens on Lake Street and Eat Street, and the cheese-filled Juicy Lucy as its local burger. Neither city has much fine dining.

Minneapolis has the stronger museums. The Minneapolis Institute of Art, with its huge collection and free general admission, and the Walker Art Center with its Sculpture Garden are worth a trip in themselves. The Mill City Museum and the Stone Arch Bridge tell the flour-milling story beside St Anthony Falls.

Denver's sights are fewer and more Western. Around Civic Center Park are the gold-domed Capitol, the Denver Art Museum with its Native American collection, and the Clyfford Still Museum. The brick warehouses of LoDo and Union Station are close by. They fill a good couple of days, but the list is shorter.

A night out is much the same in both: bars and brewery taprooms rather than clubs, and bars close at 2am. Denver has a bit more edge in places, from game-night crowds in LoDo to the dive bars of East Colfax, and at altitude each drink counts for more. Minneapolis is at its best on summer patios and rooftops in the North Loop and Northeast, but its streets empty out in winter.

This is Denver's great advantage. The Rockies start at its western edge. Red Rocks and the foothills at Golden are about half an hour out, there are summits over 4,000m, and the tundra and elk of Rocky Mountain National Park are a day trip away. In winter there are big ski areas too.

Minneapolis is green rather than wild. The 80km Grand Rounds links lakes, Minnehaha Falls and the Mississippi gorge for cycling and paddling, and the bluffs of the St Croix are an hour away. But the land is flat and there is nothing to climb.

Denver has more to drive out to. Boulder under the Flatirons, the Victorian mining towns of Georgetown and Idaho Springs, Manitou Springs and Estes Park all make easy days out of very different kinds, most with mountain scenery on the way.

From Minneapolis the best trip is to St Paul, a light-rail ride away, with its Capitol and the mansions of Summit Avenue. The river towns of Stillwater and Red Wing are also within reach, but beyond them the land within two hours is mostly farmland.

Both cities are easy with children, and each has a zoo, a science museum and a children's museum. The difference is the setting. Denver keeps its zoo and the Museum of Nature & Science together in City Park, and older children can ride the scenic railways and explore the old mining towns. With small children, take the altitude and sun seriously.

Minneapolis leans indoors. The amusement park and aquarium at the Mall of America are on the light rail, which suits a winter visit, and in summer there are lake beaches and paddle boats.

Minneapolis is the easier city without a car. Light rail runs from the airport to downtown, the Mall of America and St Paul. The skyways carry you across downtown in winter, and protected bike lanes and the Midtown Greenway reach the lakes.

Denver's centre is compact and walkable. A free shuttle runs along the 16th Street Mall and a train comes in from the airport. But the mountains, Red Rocks and nearly every day trip need a hired car.

Minneapolis is the better city for shopping, mostly because of the Mall of America. It is reachable by light rail, and there is no sales tax on clothing. The North Loop and Northeast add independent boutiques and makers' studios.

Denver's best buys are specialist: big outdoor-gear stores and Western wear, from boots to hats. There are also the upscale mall and boutiques of Cherry Creek and the vintage shops of South Broadway. Neither city has much luxury retail.

Neither city is cheap for visitors from abroad, but Minneapolis is the gentler of the two. Hotels cost moderate amounts by American standards. The Minneapolis Institute of Art, the Sculpture Garden and the lakes are free, and you can get around on cheap light rail without a car.

Denver's downtown hotels cost more, especially in ski season, and most visits add the cost of a hired car. Taquerias, breweries and the free trails help, but your budget goes less far.

Both are strong for live performance, in different ways. Denver's draw is Red Rocks, where a summer concert between sandstone monoliths feels like a pilgrimage. Behind it are the Denver Center for the Performing Arts, which covers several blocks, and the jazz rooms of Five Points.

Minneapolis is the deeper theatre city. The Guthrie leads a circuit that runs from children's theatre to new work, and there are the Minnesota Orchestra and First Avenue, Prince's club, for rock. It is good all year round, while Red Rocks is a summer affair.

Denver unwinds in hot water. The historic mineral pools and steam caves of Idaho Springs are under an hour west, and the larger hot-spring resorts deeper in the mountains make good overnight trips.

Minneapolis has Nordic heat instead: in winter, public saunas are set up on the frozen lakes, with a cold plunge or a roll in the snow between rounds. In summer, the local way to wind down is a walk around a lake at dusk.