Hakone or Osaka?

Neither city is a beach destination, and Hakone is the weaker of the two. You cannot swim in Lake Ashi, the shore at Odawara is steep and pebbly, and the nearest sand worth the trip is the sheltered bay at Atami, under an hour away.

Osaka does a little better. Suma near Kobe and the beaches south towards Wakayama are about an hour by train and open properly in July and August, with water warm enough for a comfortable swim. The coarse sand and suburban setting still make them an afternoon out rather than a reason to go.

In Hakone the good food is the kaiseki dinner and Japanese breakfast that come with your inn, many small seasonal courses served in private. Outside the inns there are soba and tofu shops in Yumoto, the black eggs at Owakudani and set meals for day-trippers, and most of these places close by early evening.

Osaka is in a different class, and many people go just to eat. You can snack on takoyaki and grilled scallops along Dotonbori and in Kuromon Market, cook okonomiyaki at your table and eat kushikatsu in Tenma, then book a counter in Kitashinchi for sushi or kappo at the highest level. It is generous and good value at every level.

Hakone's sights are scattered around the caldera and lean towards art in landscape. Sculpture fills the lawns of the Open-Air Museum, the Pola Museum keeps Impressionist paintings in the beech woods, and Tokaido history survives at the rebuilt Sekisho checkpoint and the shrine gate standing in the lake.

Osaka has more to see and more variety. It has the castle on its original stone walls, the ancient foundations of Shitennoji, the arched bridge at Sumiyoshi Taisha and the Korean and Chinese ceramics on Nakanoshima. The modern city is a sight in its own right, from the neon of Dotonbori to the old streets of Shinsekai under Tsutenkaku tower.

After dinner, Hakone means a last bath and bed. A handful of izakaya in Yumoto stay open a little later, but up the mountain the villages go quiet, and that is part of the appeal.

Osaka is known across Japan for its evenings. You can work through the standing bars of Ura-Namba, the DJ bars of Amerikamura and the tiny bars in the lanes around Ohatsutenjin, chatting with strangers at the counter, and many people stay out until the first train.

Here Hakone is clearly ahead. The whole stay is inside a volcanic national park, with sulphur vents steaming at Owakudani, Lake Ashi filling the crater floor and Fuji rising behind it when the cloud lifts. You can see it on foot along ridge paths, through the pampas grass of Sengokuhara and under the cedars of the old highway.

Osaka itself is flat and built up, and its green space is mostly the castle park and the riverbanks. You need a train ride to reach the waterfall trail at Minoo or the ridges of Rokko, and these are good day hikes rather than real wild country.

Both cities make good bases, and Hakone's list is good. Tokyo is within two hours on the Romancecar, Kamakura and Yokohama make easy days out, and the Izu Peninsula and the Fuji lakes lie over the ridges.

Osaka's position is almost unbeatable. Kyoto is under half an hour away, Nara and Himeji not much further, and Kobe, Uji and the monastery mountain of Koyasan are all easy by train, so a two-week stay would not run out of places to go.

Children love Hakone's journey itself: the zigzag railway, the ropeway over the steaming vents, the pirate ship on the lake and the seal shows at Hakone-en. After that there is little made for them, the communal baths are nude, and the steep paths are hard with a pushchair.

Osaka can fill a week with children. It has Universal Studios Japan, the whale sharks at Kaiyukan, Tennoji Zoo, Kids Plaza and the Expo '70 park, and lifts and baby rooms make stations and department stores easy to manage.

In Hakone the transport is part of the sightseeing, with one pass covering a loop of mountain railway, cable car, ropeway, boats and buses. It is slow, though. The villages are far apart on winding roads, and at weekends and in the autumn-colour season you queue at the ropeway, so it helps to send your luggage ahead.

Osaka is quicker and simpler. The Midosuji line runs through every central district, one IC card covers the city and the lines to Kyoto and Nara, and the flat streets are good for walking or cycling. The only real headache is changing trains in the underground maze at Umeda.

Hakone has one craft worth taking home, the yosegi-zaiku wood marquetry made in the workshops of Hatajuku, plus the sweets and pickles of Yumoto's main street. For fashion you need the bus to the outlet mall near Gotemba.

Osaka offers far more. There is fashion and cosmetics in the long Shinsaibashi-suji arcade, flagship stores on Midosuji, vintage clothes in Amerikamura and electronics and anime in Den Den Town. Kitchen knives from Sennichimae Doguyasuji are the souvenir to remember.

Hakone is the dearer stay, because the reason to go is a night at a ryokan with dinner and a bath, and the better rooms with private outdoor baths cost a lot. Simple inns and hostels in Yumoto, soba lunches and public day-baths keep the cost down, and the transport pass is good value.

Osaka is easier on the wallet, especially for food: noodles, set lunches and izakaya are cheap even in the busiest districts. Rooms are the main expense, and a compact business hotel a little outside Namba or Umeda keeps that under control.

Hakone has no theatre, concert hall or regular live music, and at most you might catch a small museum concert or a performance laid on at an inn.

Osaka is the home of bunraku, staged at the National Bunraku Theatre with English guides, and of manzai comedy in the Namba theatres, which is performed entirely in Japanese. Orchestras play at Festival Hall and Symphony Hall, small live houses host rock and jazz, and the Takarazuka Revue is a short train ride away.

Hakone is built around bathing. Hot-spring areas are spread from riverside Yumoto to the milky sulphur water of Sengokuhara, and the routine of soaking outdoors under maples, putting on a yukata and eating an early dinner slows everything down, especially midweek in autumn or winter.

Osaka does have baths, from old neighbourhood sento to large super sento with saunas and open-air pools, and the historic springs of Arima are about an hour away. But the city around them is fast and noisy, so a soak there is a break at the end of a busy day rather than a whole trip.