Nagasaki or Tokyo?

Neither city is a place to swim, and in both the real beaches are about an hour out of town. From Nagasaki that means the clean, sandy bay at Takahama on the Nomo coast, facing the open sea, or a short ferry ride to the small resort beach on Iojima.

Tokyo's swimmers take the train to the Shonan coast, to the dark volcanic sand of Yuigahama, Zushi and Enoshima. That coast is easy to pair with Kamakura's temples, but on summer weekends it fills with day-trippers from the capital. Nagasaki's water is a little warmer and its season runs into early September, though jellyfish arrive late in the summer.

Nagasaki's food is distinctive rather than deep. Centuries of foreign trade gave it champon, sara udon, castella and the shippoku banquet, and the fish in the Shianbashi izakaya is excellent. Still, the range is narrow and there is little fine dining.

Tokyo is one of the great food cities of the world. You can eat at standing soba counters, at sushi and tempura specialists who have made one dish for decades, or in kaiseki rooms, and you can spend whole afternoons in the depachika halls and the Tsukiji outer market. A food lover could eat for weeks in Tokyo and only a few days in Nagasaki.

Nagasaki tells a story no other Japanese city can. The Atomic Bomb Museum and the Peace Park sit alongside Dejima's Dutch trading post, Oura Cathedral, the Glover Garden merchant houses and the Ming-style Sofukuji temple. It is focused and moving, and two or three days cover it.

Tokyo's heritage is more scattered, because the 1923 earthquake and the 1945 bombing destroyed most of the old city. It still offers far more to see: Senso-ji, Meiji Jingu and the Imperial Palace moats, and above all Ueno's museums, led by the Tokyo National Museum's vast collection of Japanese art. Its modern architecture is worth seeing in its own right.

A night out in Nagasaki means Shianbashi: izakaya, karaoke and snack bars that mostly serve their regulars. The streets empty well before midnight, and many visitors spend the evening on the night view from Mount Inasa instead.

Tokyo's nights are on a completely different scale. You can move from Omoide Yokocho's yakitori stalls to the two hundred tiny bars of Golden Gai, or to whole buildings of bars devoted to whisky or vinyl. The clubs in Shibuya and Roppongi keep going until the first trains.

Nagasaki's landscape starts at your door. The city climbs steep green hills around a deep harbour, and the ropeway up Mount Inasa gives the famous night view. Further out are the rocky Nomo coast, the volcanic peaks of Unzen about two hours away and the wooded Kujukushima islands, best seen by kayak.

Tokyo is mostly city, but its trains reach a wider and grander range of outdoors. Mount Takao is an easy first hike, the Okutama valleys have gorges and cedar ridges, and Hakone and the Fuji Five Lakes give the classic views of Mount Fuji, with the climb itself possible in July and August.

Nagasaki's best outing is the boat to Gunkanjima's concrete ruins, though landings depend on the weather. Shimabara's samurai street, the porcelain towns of Arita and Imari and the Dutch-themed Huis Ten Bosch resort are all rewarding, but most of them take a long day.

Tokyo's rail network puts much more within easy reach. Kamakura's Great Buddha and Zen temples, Nikko's Toshogu shrine, Yokohama's harbour and the old merchant streets of Kawagoe are all simple trips. Hakone's hot-spring inns and lake boats round out a list you could fill a week with.

Nagasaki pleases children in a modest way, with the trams, the Inasa ropeway and the Penguin Aquarium, where the birds waddle out onto a small beach. But its stepped hillside lanes are hard work with a pushchair, and the Atomic Bomb Museum needs some care with younger children.

Tokyo is one of the easiest big cities in the world with children. Disneyland and DisneySea, the Ghibli Museum, Ueno Zoo and the hands-on Miraikan could fill a fortnight. Stations with lifts and baby rooms, and clean toilets everywhere, make each day simpler, though rush-hour trains and the August heat are best avoided.

Nagasaki is simple: a handful of flat-fare tram lines along the valley floor link the station, Peace Park, Dejima, Chinatown and Glover Garden. Anywhere off the flat means climbing long flights of steps.

Tokyo's metro and overground lines form the densest rail network anywhere, with English signs and trains that run to the minute. Between stations are neighbourhoods that are a pleasure to walk. The only real hurdles are huge stations like Shinjuku on the first day, and the last train at around midnight.

In Nagasaki, shopping means the covered Hamanomachi arcade and a mall by the station. The things to take home are local: boxed castella, Nagasaki glass and porcelain from Hasami, Mikawachi and Arita.

Tokyo may be the best city in the world to shop. Ginza has the luxury houses and Mitsukoshi, Harajuku and Shimokitazawa have vintage clothing and independent labels, and there are specialist districts for knives, books and electronics. Even a stationery shop can fill an afternoon.

Nagasaki is the easier city on a moderate budget, mostly because rooms cost less. Business hotels near the station are fairly priced, and a day of trams costs little. The spending comes from the Gunkanjima boats, the ropeway and evenings of sake and sashimi.

Tokyo is cheaper to eat in than its reputation suggests, with ramen, set lunches and convenience-store meals. Its central rooms, though, are small and expensive, and prices climb in cherry-blossom season and Golden Week.

Nagasaki's great show is a festival. The Kunchi at Suwa Shrine every October brings dragon dances and ship floats, and the Lantern Festival lights up Chinatown around Chinese New Year. Outside those dates there is little to plan around.

Tokyo has stage life all year. Single-act kabuki tickets at the Kabuki-za, Noh theatres, the Takarazuka Revue, the NHK Symphony, opera at the New National Theatre and hundreds of small live houses in Koenji and Shimokitazawa mean there is something on every night.

In Nagasaki itself there are only a few baths and sento. The proper soaking happens on the Shimabara peninsula, at Obama's seaside footbath or among Unzen's steaming vents, and both are best with a night in a ryokan.

Tokyo builds bathing into daily life. Hundreds of neighbourhood sento, some fed by dark mineral spring water, and large sauna complexes are easy to fit around sightseeing, and Hakone's mountain onsen are about ninety minutes away. Nagasaki's quiet hillside temples offer their own calm, but Tokyo gives far more ways to unwind. In both, check the tattoo rules before you go.