Hakone or Kanazawa?

Neither city is a beach destination, though Kanazawa has the sea close at hand. Long sandy beaches run along the coast at Uchinada and Chirihama, where cars drive on the hard sand, and the water is warm enough for a half-day swim in July and August.

Hakone lies in a caldera, and swimming in Lake Ashi is not allowed. A swim means going down to Atami's sheltered sand, under an hour away. In Hakone, the water you get into is volcanic, not salt.

In Hakone the meal that matters is dinner at your inn: a kaiseki procession of mountain vegetables, river fish and tofu that can be superb. Away from the ryokan it comes down to soba and tofu shops in Yumoto, black eggs at Owakudani and set lunches by the lake, and most places close early.

Kanazawa is a food city in its own right. Omicho Market serves sweet shrimp, nodoguro and, in winter, snow crab. Kaga dishes such as jibuni, teahouse wagashi and sake from the Kaga plain round it out, and Katamachi's izakaya give you somewhere to eat every night of a longer stay.

For sightseeing, Kanazawa gives you much more. Hakone's culture comes in separate pieces around the mountain: a sculpture park on open lawns with its Picasso collection, the Pola's Impressionists in the forest, and what is left of the Tokaido, including a paved stretch under the cedars, the reconstructed barrier station and the shrine gate standing in the lake. Each is worth seeing, but you reach them one at a time by bus, boat or ropeway, and you will have seen them all quite quickly.

Kanazawa is a whole city of sights. The air raids missed it, so it still looks like the rich castle town of the Maeda lords, and a single walk takes you past Kenroku-en, the castle walls, the wooden teahouse streets of Higashi Chaya and the samurai lanes of Nagamachi. The 21st Century Museum and the D.T. Suzuki Museum add a modern side with more range than Hakone's art collections, fine as those are.

Hakone's evenings end with a last bath and a yukata. Apart from a few small izakaya in Yumoto, there is nowhere to go.

Kanazawa's Katamachi and Kigura-machi lanes are packed with izakaya, sake bars, snack bars and whisky bars that stay busy late at weekends. It is a night of drinking and talking rather than clubbing, but it is a real night out.

Hakone's landscape is the reason to go. The sulphur vents of Owakudani, the crater lake of Ashi and Fuji on clear days are all within the national park, and trails to Mount Kintoki, Komagatake and the Sengokuhara grasslands start nearby.

Kanazawa has easy walks along the Sai and Asano rivers and wooded hills at its edge. Its big landscapes are further out, though: alpine Hakusan is two hours away and the Noto coast further north, and both are hard to reach without a car.

Both are good bases for days out, but they lead in different directions. From Hakone the trips are urban and historic: Tokyo, Yokohama and Kamakura's Great Buddha, with Odawara's castle and the Izu Peninsula's spa towns closer by.

From Kanazawa the trips go into rural and religious Japan. The thatched villages of Shirakawa-go and Gokayama, the merchant streets of Takayama and the Zen monastery of Eihei-ji are the highlights, and the Shinkansen puts Takaoka's temple within half an hour.

Hakone is the better choice with children, because the transport is the fun. They can ride the zigzag railway, the cable car, the ropeway over steaming vents and the pirate ship across the lake, then see the seals at Hakone-en and climb the net sculptures. A swimsuit onsen park gets around the nude communal baths.

Kanazawa is safe and easy, and the pool installation at the 21st Century Museum and the ninja temple's trap doors go down well. But the core of a stay is gardens and teahouses, and the zoo and the Fukui dinosaur museum mean leaving the city.

Both are easy without a car, but in different ways. In Hakone, one regional pass covers a loop of mountain railway, cable car, ropeway, boat and bus, and the ride is part of the sightseeing. The villages are far apart, though, and weekend queues slow everything.

Kanazawa's main sights sit in a flat band about 2km from the station, so you can mostly walk, with loop buses and bike share to fill the gaps. Winter snow and slush are the main hindrance.

Hakone has one craft worth buying, yosegi-zaiku wood marquetry from the Hatajuku workshops, plus snacks in Yumoto and the outlet mall over the ridge at Gotemba.

Kanazawa offers a whole range of crafts: gold leaf, which it makes almost all of in Japan, along with Kutani porcelain, Kaga yuzen silk and Ohi tea bowls, with work by serious makers at the prefectural craft centre. The department stores at Korinbo and the boutiques of Tatemachi cover everyday shopping as well.

Hakone's main attraction, the ryokan night with dinner and a private bath, is also its main expense, and weekends and autumn cost the most. You can keep costs down with a hostel in Yumoto, soba for lunch and the day-bathhouses, and the transport pass is good value.

Kanazawa is easier on the budget. It has plenty of business hotels by the station, and set lunches and conveyor-belt sushi keep meals cheap. The splurges are optional: snow crab, kaiseki and a ryokan night in the Kaga onsen towns.

Hakone has no theatre or concert hall, and apart from an occasional performance at an inn, you would go to Tokyo for a show.

Kanazawa has more than its size suggests. There is Noh at the prefectural theatre, and geisha dance and shamisen in the chaya teahouses. The Orchestra Ensemble Kanazawa plays a regular season beside the station, so an evening can be planned around the programme.

In Hakone, bathing is the whole stay. Seventeen hot-spring areas, from riverside Yumoto to the milky waters of Sengokuhara, mean an outdoor bath under the cedars is never far away, often right on your balcony.

Kanazawa offers calm as much as hot water: early mornings in Kenroku-en and matcha in a teahouse. A proper soak means Yuwaku, half an hour out, or an overnight stay in the Kaga onsen towns, although many city hotels have their own hot-spring baths.