Baden-Baden or Genoa?

This is where the two part company most completely. Baden-Baden is inland at the edge of the Black Forest, and its swimming comes down to outdoor pools and the flooded gravel pits of the Rhine plain, fine for cooling off but never a reason to go.

Genoa puts the sea within a bus or train ride of every hotel: the pebble cove at Boccadasse, the bathing establishments along Corso Italia, the rock platforms at Nervi, and better bays at Camogli, Santa Margherita and Sestri Levante. Expect pebbles, paid loungers and busy summer weekends, but a daily swim is easy.

Genoa is the stronger city to eat in. It is the home of pesto, and the old town's friggitorie and farinata shops, the Mercato Orientale and the harbour trattorias serving fish with Vermentino make good, very local eating easy and inexpensive at every meal.

Baden-Baden offers Baden's hearty regional cooking, Flammkuchen, venison, Black Forest ham and cherry gateau, with a French accent from across the Rhine. Its best asset is wine, Riesling and Pinot Noir in the taverns of the Rebland villages, and the celebrated restaurants of the northern Black Forest offer a level of fine dining Genoa lacks. In town, though, the choice is narrow and leans towards hotel dining and cake.

Genoa has far more to see. Its medieval quarter of shaded caruggi is among the largest in Europe, the Rolli palaces of Via Garibaldi and Via Balbi hold Van Dyck and Rubens in painted halls, and San Lorenzo, the Palazzo Ducale and the marble sculpture of Staglieno could fill several days.

Baden-Baden's appeal is the setting itself: an intact Belle Époque spa town with the Kurhaus, the Trinkhalle and hillside villas, plus the Museum Frieder Burda and the Kunsthalle for art. It is elegant and coherent, but a day or two covers it.

Neither city is a place for clubbing, but Genoa at least has evenings out in the street. Students and locals fill the bars around Piazza delle Erbe, the waterfront at Porto Antico and Foce stays busy, and summer brings beach clubs along Corso Italia.

Baden-Baden's night out is the gilded casino in the Kurhaus, with a dress code, followed by a hotel or wine bar. The town is quiet by late evening, and anyone wanting more goes to Karlsruhe or Strasbourg.

Both have fine walking from the edge of town, but Genoa adds the sea to its hills, and that gives it the edge. Trails link the ridge forts above Righi, the Portofino promontory has cliff paths down to San Fruttuoso, the Cinque Terre terraces are a train ride away, and boats go out to watch whales and dolphins.

Baden-Baden's outdoors is wooded upland: the Merkur funicular and the Battert cliffs for climbers, fir forest trails, vineyard walks in the Rebland, and the Black Forest High Road up to the Mummelsee and the Hornisgrinde moorland. It also has modest winter skiing, which Genoa cannot offer.

Both are excellent bases, and the difference is in character. Baden-Baden's outings cross a border and several regions: Strasbourg and the Alsace wine villages, Heidelberg, Freiburg, the cathedral at Speyer and the monastery at Maulbronn. That means cathedrals, castles and wine country, but a car makes many of them easier.

Genoa's best trips run along a single railway line by the sea, to Camogli, Portofino and the Cinque Terre in one direction and Finale Ligure and Noli in the other, with no car needed. Milan and Turin are close enough for a museum day, so it mixes coastal villages with big-city art.

Genoa works better with children, mainly thanks to the Porto Antico, where the large aquarium, the science centre, the biosphere and the walk-through submarine at the Galata museum fill a full day. Funiculars and public lifts are fun in themselves, though the steep, dark lanes are hard work with a pushchair.

Baden-Baden is safe, clean and calm, with the Merkur funicular and forest trails to enjoy, but it is built for adults, and the Friedrichsbad does not admit young children. Families use it as a quiet base for days at Europa-Park or Karlsruhe's zoo.

Getting around is about as easy in both, in different ways. Baden-Baden's centre is compact enough to walk from the baths to the museums, with buses to the outlying station, but the Black Forest and Alsace really need a car.

Genoa is a climb, and the old town is a maze, but funiculars, a rack railway, public lifts and a short metro line do the work, and the coastal railway reaches the Riviera so easily that driving is better avoided altogether.

Genoa offers a little more range, from the arcades of Via XX Settembre and the labels along Via Roma to old-town shops selling candied fruit, pesto and olive oil and workshops making silver filigree and coral. Baden-Baden is smaller but more upmarket, with jewellers, watchmakers and boutiques on Sophienstraße and Lange Straße and few souvenirs beyond cuckoo clocks and wine. Neither is worth a trip just for shopping.

Genoa is noticeably cheaper. Focaccia and farinata make quick meals cost very little, trattoria lunches are fair and central hotels cost less than in Italy's busiest cities, though Riviera resorts and loungers cost more in summer.

Baden-Baden was built for wealthy visitors and still prices for them: grand hotels set the tone, and every visit to the baths costs extra. Guesthouses and wine taverns soften the bill, but a stay centred on the spas soon adds up.

Baden-Baden has the more remarkable classical calendar for its size. The Festspielhaus, one of Germany's largest concert halls, brings top international orchestras and opera, and the Kurhaus and the small nineteenth-century theatre continue a line that runs back to Brahms and Clara Schumann. Beyond classical music there is little.

Genoa has a solid opera house in the Teatro Carlo Felice, Paganini concerts and an established drama company performing in Italian, plus small clubs that keep the city's singer-songwriter tradition alive. It is broader in range, but not something to build a trip around.

Baden-Baden is the obvious choice for rest. Roman-era springs feed the domed Friedrichsbad, with its silent sequence of hot rooms and pools, and the modern Caracalla complex next door, and the rest of the town moves at the same slow pace of hotel spas, park walks and early nights.

Genoa has no bathing tradition of its own, so spas mean hotel facilities, and the nearest thermal water is at Acqui Terme, over an hour inland. For calm, try the Nervi gardens or a long lunch in a Riviera village, since the port city itself is anything but restful.