Hakone or Tokyo?

Neither place is a beach destination, though Tokyo comes closer. From the capital, direct trains run in about an hour to the Shonan coast, where Yuigahama, Zushi and Enoshima offer long stretches of dark volcanic sand, and Odaiba's man-made shore is pleasant for a stroll.

Hakone has no swimming of its own. Lake Ashi is off limits and the coast below at Odawara is steep and pebbly, so a swim means heading on to Atami's sheltered sand for a summer outing.

Food is where Tokyo pulls furthest ahead. Its range runs from station soba counters and one-dish specialists to Tsukiji's outer market, the yakitori alleys of Yurakucho and more Michelin-starred restaurants than any city on earth, and good food is easy to find at any hour.

Hakone's best meal is the kaiseki dinner served at your inn, which can be superb, but beyond the ryokan you are left with soba and tofu shops in Yumoto, black eggs at Owakudani and lakeside set meals, most of them closed by early evening.

Tokyo offers far more to see. Ueno Park alone holds the Tokyo National Museum and the National Museum of Western Art, and Senso-ji, Meiji Jingu, the Imperial Palace moats and the lanes of Yanaka add heritage spread across the modern city.

Hakone's sights are fewer but distinctive for a mountain resort: the sculpture lawns of the Open-Air Museum, the Pola Museum in its beech forest, the rebuilt Sekisho checkpoint and the torii gate standing in Lake Ashi. Two unhurried days cover them all.

The two could hardly be further apart after dark. Tokyo has Golden Gai's two hundred tiny bars, smoky Omoide Yokocho, whisky and vinyl bars in every district and clubs in Shibuya and Roppongi that run until morning.

In Hakone, the evening is a bath and an early night, with only a handful of izakaya in Yumoto staying open a little longer.

Hakone has the better landscape on the doorstep. You are inside a volcanic caldera in a national park, with steaming sulphur vents at Owakudani, Lake Ashi ringed by forest, Fuji on clear days and trails leaving straight from the villages, and the seasons change it sharply, from hydrangeas in early summer to red maples in November.

Tokyo's green spaces inside the city are parks and gardens such as Shinjuku Gyoen and Yoyogi. The real hills, Mount Takao and the Okutama gorges, lie an hour or more away by train.

Both make good bases, and they share Kamakura and Yokohama within easy reach. The difference is the direction you head in. From Hakone the natural outings run south and west, to Odawara's castle, Atami and the temple towns of Izu, or over the ridge to the Fuji lakes, and Tokyo itself is a day trip on the Romancecar.

Tokyo's fast lines open up the north instead: the shrines of Nikko, the merchant streets of Kawagoe, canal-side Sawara and Karuizawa by shinkansen, with Hakone as one of its own classic outings.

Tokyo is much the easier choice with children. Disneyland and DisneySea, the Ghibli Museum, Ueno Zoo and the hands-on Miraikan can fill a week, and lifts, baby rooms and spotless toilets in every station make daily life simple.

Hakone works for a short stay of two or three days. Children love the zigzag railway, the ropeway over the vents and the pirate ship across the lake, but formal inns, nude communal baths and steep paths that defeat a pushchair make it harder going.

Tokyo's dense network of metro, overground lines and the Yamanote loop puts nearly every sight a short walk from a station, and the neighbourhoods between are pleasant to walk. Its only snags are crowded rush hours and huge stations that confuse at first.

Hakone needs no car either, since one pass covers the mountain railway, cable car, ropeway, lake boats and buses, and the loop is a sight in itself. It is slow, though, with villages kilometres apart and queues at the ropeway at weekends.

Tokyo is a destination for shopping in its own right, from the department stores of Ginza and Omotesando's flagships to vintage in Shimokitazawa, knives on Kappabashi, books in Jimbocho and electronics in Akihabara.

Hakone has one craft worth seeking out, the yosegi-zaiku wood marquetry made around Hatajuku, plus sweets and pickles along Yumoto's main street. Anyone wanting fashion has to take the bus to the outlet mall near Gotemba.

Tokyo is the easier place to keep costs down, because eating out is such a bargain, from ramen and set lunches to convenience-store meals, and many shrines and parks are free. The money goes on small central hotel rooms.

In Hakone the ryokan night with dinner, breakfast and a bath is the costly heart of the visit, especially with a private outdoor bath or at weekends in autumn. Simple inns in Yumoto and public day-bathhouses soften the bill.

This is all Tokyo. Kabuki at the Kabuki-za, Noh theatres, the Takarazuka Revue, the NHK Symphony at Suntory Hall, opera at the New National Theatre and live houses in Koenji and Shimokitazawa give a choice every night.

Hakone has no theatre or concert hall, and an occasional museum recital or performance at an inn is the most a visitor will find.

Both have serious bathing cultures, but Hakone is built around them. Its hot-spring villages, from riverside Yumoto to the milky sulphur water of Sengokuhara, offer outdoor baths under maples, private baths on the balcony and slow evenings in a yukata, best midweek in autumn or winter.

In Tokyo, bathing is part of daily life in neighbourhood sento with their painted Fuji murals and in big sauna complexes, while calm comes from temple grounds and gardens between the crowds.