Hakone or Nagoya?

Neither city lets you swim on its doorstep, but Nagoya has the easier summer swim. Wide sandy beaches on the Chita Peninsula, such as Utsumi, are about an hour away by train, with small islands like Shinojima a ferry ride beyond, and local families fill them in July and August.

Hakone sits in a caldera where Lake Ashi is closed to swimmers and the shore below at Odawara is steep pebble. Atami's sheltered sand is the realistic option, a single outing rather than a choice of beaches.

Nagoya is one of Japan's distinctive regional food cities, with dishes such as hitsumabushi eel, misonikomi udon and kishimen noodles, each served by its own specialists. Add the morning-service café breakfasts, the deep department-store food halls and Osu's street snacks, and you can eat something different at every meal.

Hakone's strength is narrower. The kaiseki dinner at a good inn can be superb, but beyond it there are soba and tofu shops in Hakone-Yumoto, black eggs at Owakudani and set meals by the lake, most of them shut by early evening.

Nagoya has more history to see in one place. The rebuilt castle and its painted Honmaru Palace, Atsuta Shrine in its forest and the Tokugawa Art Museum's samurai treasures sit alongside the Toyota and railway museums, which explain how industrial Japan was built.

Hakone's culture is quieter and more spread out. Its highlights are art in a landscape, sculpture on the lawns of the Open-Air Museum and Impressionists at the Pola, plus traces of the old Tokaido road at the lakeside checkpoint and Hakone Shrine's torii standing in the water.

Nagoya has a real night out, though a modest one by Japanese city standards. Sakae and Nishiki pack izakaya, tiny bars, karaoke and a few dance clubs into narrow buildings, and Friday and Saturday are lively.

Hakone has essentially nothing after dinner beyond a few small bars in Hakone-Yumoto. Evenings there are a bath and an early night, by design.

This is Hakone's ground. You stay inside a volcanic caldera in a national park, with steaming sulphur vents at Owakudani, Lake Ashi on the crater floor, ridge walks to Mount Kintoki and the cedar-lined Old Tokaido Road, all reached without leaving the area.

Nagoya sits on a flat, built-up plain, so nature in the city means parks and formal gardens. The Suzuka Mountains, Korankei's maples and the Nakasendo trail in the Kiso Valley are fine, but each takes an hour or two of travel.

Both are good bases, but Nagoya reaches further and faster. Kyoto is about 35 minutes by shinkansen, Osaka under an hour and Ise Jingu within two hours, while original castle keeps at Inuyama and Hikone and the pottery towns of Seto and Tokoname are closer still.

Hakone's outings point towards Tokyo and the coast instead: Kamakura's Great Buddha, Yokohama, Odawara's castle, Atami and the Izu Peninsula, with Tokyo itself under two hours on the Romancecar.

Nagoya is much the stronger choice with children. The port aquarium with orcas and belugas, Legoland, Ghibli Park, Higashiyama Zoo and full-size bullet trains at the railway museum could fill a week, and Nagashima's roller coasters are under an hour away.

Hakone works for a short stay built around the rides: the zigzag railway, the ropeway and the pirate ship on Lake Ashi. Beyond those, a small seal aquarium and a swimsuit onsen park, little is aimed at children, and formal inns and nude communal baths can be awkward.

Hakone's mountain railway, cable car, ropeway and lake boats all run on one regional pass and form a loop that is part of the sightseeing. They are also slow. The villages lie kilometres apart on winding roads, and at weekends and in the autumn-colour season the ropeway queues grow and the buses crawl.

Nagoya is quicker to get around. Its wide postwar grid is easy to follow, Sakae, the castle and Osu are within walking distance of one another, and one IC card covers the subway and the JR, Meitetsu and Kintetsu lines. Nagoya Station is a major interchange where the regional lines meet, so getting out of the city is straightforward.

In Hakone there is one wood craft to buy, and Nagoya has whole streets of department stores. Hakone's craft is yosegi-zaiku, a geometric marquetry of naturally coloured woods made into puzzle boxes and trays in the workshops around Hatajuku. Beyond that, Hakone-Yumoto sells sweets and pickles, and for fashion you take a bus over the ridge to the outlet mall near Gotemba.

Nagoya has far more range. Large department stores stand around Sakae and above the station, with international brands on the avenues between them, while Osu's covered arcades around the Kannon temple mix secondhand clothing, anime and electronics. For something made locally, look for Arimatsu shibori tie-dye and pottery from Seto and Tokoname.

Nagoya is the less expensive stay of the two, and most of the difference lies in the bed. In Hakone the night people come for is a ryokan, with dinner, breakfast and the hot-spring bath bundled into one bill, and that bill climbs steeply at the better inns, at weekends and in autumn. Nagoya's many business hotels offer a plain room for far less and leave you free to eat cheaply in noodle shops or over a morning-service breakfast.

Hakone narrows the gap if you settle for a simple inn near Yumoto and the public day-bathhouses, and once you have a bed its regional pass keeps the days themselves modest. Nagoya's costs sit elsewhere: eel dinners, shinkansen trips to Kyoto and the theme parks are what stretch a budget there.

Nagoya has a full programme: opera and touring orchestras at the Aichi Arts Center, kabuki at the Misono-za, Noh near the castle and jazz in small live houses around Sakae. Much of it is aimed at Japanese speakers, so check what is on before you plan an evening.

Hakone has no theatre or concert hall at all. The most you will find is an occasional museum concert or a performance at an inn.

Hakone is one of Japan's great places for bathing. Its hot-spring villages range from riverside Yumoto to the milky sulphur water of Sengokuhara, many inns have a private bath on the balcony, and the slow pace is the point. A midweek stay avoids the Tokyo day-trippers.

Nagoya makes bathing easy rather than special. City sento and large super sento with saunas are easy to drop into, and Tokugawaen's ponds offer calm, but a classic onsen stay means two hours by train to Gero.