Milwaukee or Washington DC?

Neither city is a beach destination, but Milwaukee at least has beaches of its own. Bradford Beach and the smaller McKinley and South Shore beaches are on Lake Michigan, which is fresh water. Bradford has sand volleyball and cabanas, but the lake is cold outside late June to early September and many visitors only paddle.

Washington has no beach at all. The Potomac is not for swimming, the small brackish beaches around Annapolis are an hour away, and the Atlantic resorts need a weekend. In summer, a hotel pool is the realistic way to cool off.

Washington eats more widely and more ambitiously. It has Ethiopian cooking around Shaw and U Street, pupusas in Columbia Heights, Chesapeake crab and oysters in season, and serious tasting menus around Logan Circle and Penn Quarter. Milwaukee can't match that range.

Milwaukee's strength is tradition. It has the Friday fish fry, the supper club with its relish tray, frozen custard and bratwurst, and a brewing history that runs from the old brewery buildings to the taprooms of Walker's Point. The food is hearty and full of character, but there is little fine dining.

This is the widest gap between the two cities. Washington's Smithsonian museums, the National Gallery and the monuments from the Capitol to the Lincoln Memorial fill a week, and most of them cost nothing to enter.

Milwaukee has a shorter, more personal list. There is the Art Museum in Calatrava's lakefront pavilion with its moving sunscreen, the Harley-Davidson Museum, the Pabst Mansion and the domed Basilica of St Josaphat. Two or three days covers it comfortably.

Washington has the bigger night out, kept busy by young staffers and students. It has cocktail bars and rooftops on 14th Street and U Street, a late strip in Adams Morgan, riverside beer gardens at the Wharf, and a few clubs that bring in touring DJs at weekends.

Milwaukee's nightlife is a different kind. The real draw is its corner taverns, with pool tables and old brewery signs. Water Street is for the sports crowd and Brady Street for dive bars, but there is little clubbing and winter evenings are quiet.

Washington has more within reach. Rock Creek Park runs through the city, the C&O Canal towpath follows the Potomac, the gorge at Great Falls is half an hour upriver, and Shenandoah's ridge hikes are within two hours. Spring blossom and autumn colour are the highlights, with a sticky summer in between.

Milwaukee's outdoors is gentler and centred on Lake Michigan. There is Olmsted's Lake Park, long flat rides on the Oak Leaf Trail, kayaking on the river through downtown, and the glacial hills of Kettle Moraine an hour away. Outdoor life mostly runs from May to October.

Each city has a bigger neighbour within easy reach: Chicago by train from Milwaukee, and Baltimore or Philadelphia from Washington. The difference is in the places closer by.

Washington is surrounded by history: Old Town Alexandria by Metro, Mount Vernon, Annapolis, and the battlefields of Gettysburg, Antietam and Harpers Ferry. Milwaukee's nearby trips are quieter, with Madison, the old mill-town main street of Cedarburg, Frank Lloyd Wright's buildings in Racine and the gardens at Kohler. Beyond those it is farmland.

Washington is the better choice with children, mainly because its best attractions are free and built to teach. There are the dinosaurs at Natural History, the rockets at Air and Space, the National Zoo and the open lawns of the Mall. Every Metro station has lifts, which makes buggies easy, though summer walks between the monuments are hot.

Milwaukee is relaxed and easy to drive around, with a well-regarded county zoo, Discovery World's aquariums and the Mitchell Park Domes. It is much less appealing for families in the long winter.

You can see Washington without a car. The Metro reaches most sights as well as Arlington, Alexandria and the airport, and bike-share docks line the riverside paths. Georgetown, with no Metro station, is the one awkward spot.

Milwaukee's walkable centre is small: downtown, the Third Ward and the Riverwalk, linked by The Hop streetcar. Outside it, you need a car or ride-hailing to reach the zoo or the Harley-Davidson Museum, though parking is easy.

Neither city is a shopping destination, but Washington has more to browse. There are the brick streets of Georgetown, luxury labels at CityCenterDC, the weekend stalls at Eastern Market and good museum shops. Milwaukee's best shopping is the warehouse boutiques of the Third Ward and the vintage shops on Brady Street, and most visitors leave with Wisconsin cheese, local beer or Harley-Davidson gear.

Milwaukee is much cheaper to stay in. Hotel rooms cost far less than in Washington, beer and fish fries are inexpensive, and the lakefront and many festivals cost little. Big summer weekends push room rates up, though, and a hire car adds to the bill.

Washington's hotels and restaurants are priced for expense accounts, especially in cherry blossom season. What helps is that the museums, the zoo and the memorials are free, and staying across the river in Arlington can cut the cost of a room.

Summerfest is the reason to plan a Milwaukee trip around music. For several weeks each summer it fills the lakefront festival grounds with acts on many stages. The rest of the year, the symphony, the Florentine Opera, the Milwaukee Rep and the ornate Pabst Theater put on a solid programme, though on a local scale.

Through the rest of the year Washington gives you more choice, and theatre is where it pulls ahead. Arena Stage, the Shakespeare Theatre Company, Ford's Theatre and the Folger's playhouse are joined by the National Symphony and the Washington National Opera. For music, the U Street halls bring in big touring acts, and you can also hear go-go, the city's own funk.

Neither city is good for wellness, and both offer little beyond hotel and day spas. The difference is where you find calm. In Washington it's an early walk round the Tidal Basin or the Dumbarton Oaks gardens. In Milwaukee it's the lakefront and the Riverwalk, with a proper spa day at Kohler, an hour's drive north.