Cortina d'Ampezzo or Genoa?

There is no real contest here. Cortina's alpine lakes, Ghedina and Pianozes among them, are fed by snowmelt and better for walking round than swimming in, so in practice swimming means a hotel pool. The Adriatic is more than two hours' drive away.

Genoa offers a swim most summer afternoons: the pebble cove at Boccadasse, the bathing establishments built over the rocks on the Corso Italia, and the platforms below Nervi's promenade. The prettier bays at Camogli and Sestri Levante are a short train ride away, though the shores are mostly pebble or coarse sand and rented loungers take up much of the space.

Genoa is where you eat better, and more easily. Pesto, oily focaccia, farinata and panissa from the old-town friggitorie, pansoti in walnut sauce and seafood in the harbour trattorias make the city worth visiting for its food alone, and the Mercato Orientale shows where it all comes from.

Cortina's Ampezzan mountain cooking has real character, from beetroot casunziei to polenta with game, and its best moments come on rifugio terraces among the peaks. In the valley, though, the choice is narrow and expensive, with almost no street food, while Genoa has plenty that is cheap and very local.

Genoa wins this easily. You can spend several full days on its sights: the shaded caruggi, the Rolli palaces on Via Garibaldi with their Van Dyck and Rubens canvases and painted halls, the striped Cathedral of San Lorenzo and the marble sculpture at Staglieno.

Cortina has a pleasant centre, the 1956 Olympic ice stadium and the Regole's small museums, led by the Rimoldi collection of twentieth-century art. Its most powerful history lies up in the mountains, in the First World War tunnels on Lagazuoi and the Cinque Torri, and seeing them is as much a hike as a visit.

Neither city is made for a big night out, but Genoa has more going on after dark. Students and locals keep the small bars around Piazza delle Erbe busy until late at weekends, and in summer evenings move out to the waterfront at Foce and the beach clubs along the coast.

In Cortina, evenings mean après-ski drinks, the passeggiata on the Corso Italia and long dinners. A few smart bars and clubs stay open late in the peak winter weeks, but in summer the town goes quiet early.

Both are fine places to be outdoors, but Cortina is exceptional. The Dolomites ring the town and lifts leave from the centre. The choice runs from skiing on the Superski network to the Alta Via 1, via ferrata and climbing, and the Tre Cime di Lavaredo and Lago di Misurina are under an hour away.

Genoa's outdoors are gentler and come with the sea: the fortress trail above Righi, the Portofino promontory's cliff paths down to San Fruttuoso, the Cinque Terre by train, and boat trips into the Pelagos Sanctuary to look for whales and dolphins. They are outings to fit around a city stay rather than a mountain vacation in their own right.

From Cortina, most outings lead into other mountain valleys. The best of them lie in South Tyrol, at San Candido and at Bolzano with the Iceman in its archaeology museum. Venice is possible but makes a long coach day, and the towns within range are pleasant rather than essential. Many are easier with a car.

Genoa is far better placed. Camogli and Santa Margherita are under an hour by train, Portofino is a short bus or boat ride on from Santa Margherita, and the Cinque Terre are about an hour and a half by rail. Milan and Turin are close enough for a museum day, and trains, buses and boats cover all of it without a car.

Genoa has more for children who aren't skiing. At the Porto Antico there are the aquarium, a science centre and the walk-through submarine at the Galata museum, and rides on the funiculars and public lifts help in any weather. The steep, dark lanes of the old town are hard work with a pushchair, though.

Cortina suits active families well. It has ski schools, beginner slopes at Socrepes, public skating, and easy summer walks to lakes and huts, all from a small, calm centre. Beyond the outdoors there is little aimed at children, and a wet day can feel long.

Cortina's small, flat centre takes minutes on foot. Beyond it, you depend on ski buses in winter, a limited bus service up to the passes, or a hire car. The town has had no railway since 1964, so you arrive by coach from Venice or after a long drive.

Genoa is hilly and its lanes are a maze, but funiculars, public lifts and a short metro line help. Its real advantage is the coastal railway, which reaches Nervi and the Riviera towns without a car. Buses are slow in traffic, and driving in the centre is best avoided.

Cortina's shopping is one polished strip, the Corso Italia, with luxury fashion, furriers, jewellers and upmarket mountain wear, anchored by the Cooperativa, a store that has been trading since 1893. It is smart, but once you have walked its length there is little else.

Genoa has the edge overall, simply because there is more to browse. Via XX Settembre and Via Roma carry the familiar Italian labels, though with less luxury than Cortina. The real interest is in the old town, where long-established shops sell candied fruit, olive oil and pesto and small workshops make coral and ceramics, so it is the better place for food and crafts to take home.

This is one of the widest gaps between the two. Cortina is among the most expensive places to stay in Italy. In winter and August, hotels and restaurants charge luxury-resort rates, and lift passes and equipment hire come on top. Rifugio meals and early-summer or late-September stays soften the bill only a little.

Genoa is a mid-range city that feels good value for northern Italy. Focaccia and farinata are cheap, trattoria lunches are fair, and the funiculars and buses cost little. Costs rise in the smarter Riviera resorts in summer, and loungers add up on beach days.

Genoa gives you a proper evening out. The Teatro Carlo Felice on Piazza De Ferrari stages opera, ballet and symphony concerts, the Teatro Nazionale performs drama in Italian, and there are Paganini concerts in his own city. Small clubs keep its singer-songwriter tradition alive.

Cortina has no theatre season and no regular venue. Summer festivals bring chamber and classical concerts to churches, halls and sometimes mountain settings, but outside those weeks there is little on.

Cortina is the more restful of the two, thanks to its hotels and its pace. Many hotels have Alpine spas with saunas, hay baths and indoor pools. In June, September or a quiet winter week, the clear air and an afternoon on a hut terrace do the rest, though the peak weeks bring traffic and crowds.

Genoa's centre, with its port and crowded lanes, is lively rather than calm. The quiet is at the edges: the villa gardens and promenade at Nervi, or a slow lunch in a Riviera village. The thermal waters of Acqui Terme are a little over an hour away.