Mount Takao

The Japanese have been making the pilgrimage to Mount Takao for more than 1,200 years; now they share the sacred mountain's slopes with tourists searching for "old Japan" – all within an hour of Shinjuku station. On a clear day, the 599m summit offers views of Tokyo and Mount Fuji, and the less energetic can take a cable car or chairlift halfway up the six hiking trails. Takao is still considered an important religious site, so don't be surprised to find yourself sharing a trail with ascetic Buddhists on their way to pray at Yakuo-in temple or cleanse themselves beneath the freezing waterfalls of Biwa-daki or Hebi-daki. Go in March and you can even join them in a spot of fire walking. Wait about an hour after the embers start glowing to keep pain to a minimum.

• japan-guide.com

Cycling in Yoyogi Park

Photograph: salvo severino / Alamy

Tokyo has been described as one of the best cities in the world to discover by bicycle. It's relatively flat but with enough hilly neighbourhoods to keep things interesting, and while parts of the city can become gridlocked, the air quality is pristine compared with, say, Bangkok or Hong Kong. Given its size, you could cycle for a week and still only scratch the surface of Tokyo. So where to start? The Tokyo Bay area is a favourite among locals, but for a more secluded ride, complete with clearly marked cycling lanes, Yoyogi Park, a vast expanse of greenery near the trendy Harajuku neighbourhood, is hard to beat. Tokyo Rentabike does all-day rentals for under £10.

• tokyorentabike.com. Read about the exploits of a keen Tokyo cyclist at tokyobybike.com

Tokyo Tower

Photograph: Yoshinori Kuwahara/Getty Images/Flickr RF

Poor old Tokyo Tower: it has been demolished several times by Godzilla, had its antenna bent in the 2011 earthquake and was rendered obsolete by the digital age. But as a vantage point for some of finest views of Tokyo, its future is guaranteed – for now. Located in Shiba Park, the 333m structure, modelled on the Eiffel Tower but painted orange and white to comply with air safety regulations, has two observation decks – at 150m and then 250m for those with a head for heights. Due to open across town in May is Tokyo Sky Tree, now the country's tallest man-made structure, at 634m. It's worth a trip for the view from 450m – mercifully, there's a lift – or simply to stay on firm ground and marvel at its size.

tokyotower.co.jp, adults from around £7, children £4

Jogging round the Imperial Palace

Photograph: Alamy

For the most part, Tokyoites tend to rub along nicely – no mean feat for a city of almost 13 million people. The path running around the grounds of the Imperial Palace, however, is the scene of the occasional contretemps involving pedestrians and the hordes of joggers. It's a safe distance from traffic, the views of the skyscrapers hugging the park's perimeter are impressive, and no one will sneer if you turn up in cheap running gear and proceed at a crawl. Along the route are markers for all of Japan's 47 prefectures – with a leap of imagination you could be running the length and breadth of the country. Just keep an eye out for perambulating tourists.

• cnngo.com

Yakatabune boat trip

Photograph: Atlantide Phototravel/Corbis

Yakatabune – literally roof boats – are supposed to resemble traditional Japanese homes, with their long, low tables, tatami mats and plentiful supplies of sashimi and tempura. Several companies operate yakatabune as pleasure boats in Tokyo Bay for groups who like to do their socialising at sea. In summer, a yakatabune trip is one of the best ways to view the firework festivals, while the night-time views of the island of Odaiba and the illuminated Rainbow suspension bridge are always impressive. A word of caution: the drink-all-you-can deal is enticing, but remember that a yakatabune dinner entails at least a couple of hours at sea on a fairly small boat.

• +81 3 3644 1344, harumiya.co.jp, English-speaking staff available, ¥10,500pp (around £90) including sashimi, tempura, unlimited drinks and karaoke

Odaiba-Asakusa river bus

Photograph:Jose Fuste Raga/Corbis

One of the best ways to navigate Tokyo's streets is, oddly, by boat. The Sumida river buses weave through the heart of the city to one of three destinations. The most popular route connects Odaiba and Asakusa, passing the Asahi Beer hall and its infamous "golden turd" statue. The trip is a contrast in streetscapes: the former is best known for the Rainbow Bridge and the space-age headquarters of Fuji TV, the latter a wonderfully disorderly collection of narrow streets, old buildings and Sensoji Temple, instantly recognisable by the huge akachochin red lantern marking its entrance. Wander around the street market and don't leave Asakusa without trying a beer and Denki Bran (electric brandy) chaser at the Kamiya Bar.

• suijobus.co.jp, adults around £13 single, under-12s around £8, under-6s free

Urban fishing

Photograph: Alamy

Anglers who prefer the smell of early-morning dew as they bait up would probably be horrified, but if you prefer convenience and almost guaranteed results, it is possible to catch freshwater fish right in the heart of Tokyo. The Sumida and Tamagawa rivers aside, the best option for tourists is a day at Ichigaya fish centre, a collection of five rectangular pools filled with small carp and fed by the waters of the Kanda river. Ichigaya might also appeal to those with a competitive streak: anglers weigh their catch at the end of each hour – reach 7kg and you can fish free for another hour.

• Ichigaya Tamachi 1-1, Shinjuku-ku, +81 3 3260 1324, ichigaya-fc.com/fishing, one hour costs around £6, rod and bait extra

Kamakura

Photograph: Alison Wright/Corbis

If time or budget rules out a long trip to the temples of Kyoto or the tranquillity of the far north, the best option for a mini break from Tokyo is Kamakura. The ancient capital is less than an hour from the city, but aesthetically, it's a world away. Stroll around Kamakura's cultural and natural attractions: Engakuji Temple, the Great Buddha at Kotokuin Temple and a walk along Yuigahama beach which, weather permitting, comes with a bonus view of Mount Fuji. Dining on a shojin ryori vegetarian meal will prepare you for the uphill hike to the farthest reaches of Kenchoji Temple, the most important Zen Buddhist structure in Kamakura, with breathtaking views of the city below.

• japan-guide.com

A walk in Inokashira Park

Photograph: Alamy

Tokyo has no shortage of green spaces, and Inokashira Park, in the west of the city, is among the best. It's easily navigable on foot, but large enough to stay interesting, with a forest, a boating pond, sports facilities, and a small zoo and aquarium. At weekends and holidays there's an art market. It is also home to Ghibli Museum, devoted to the studio behind Hayao Miyazaki's much-loved anime films such as Spirited Away. The park also benefits from its proximity to Kichijoji, a neighbourhood popular among young Tokyoites, who flock to its bars, restaurants and clubs.

• ghibli-museum.jp/en, adults around £8.50, reduced rates for children depending on age, make sure to reserve before leaving for Japan. Open Wed-Mon 10am-6pm

Hakone

Torii Gate at the Hakone Shrine. Photograph: Atlantide Phototravel/Corbis

For all their charms, Tokyo's urban onsen are ultimately a poor imitation of the hot-spring resorts found all over Japan. Immersion in a genuine onsen is as easy as jumping on a train at Shinjuku bound for Hakone, 70 minutes away. Most of Hakone falls within a volcanically active national park centring on Lake Ashi, and the area is packed with public bath houses and ryokan (inns), many of which open their doors to day bathers. But to do Hakone justice, find a reasonably priced ryokan and take a couple of days to explore the volcanic geysers of Owakudani, the botanical gardens, the cherry blossom in spring and Hakone shrine on the shore of the lake.

• japan-guide.com/e/e5200.html

For more information go to the Japan National Tourism Organisation's website: jnto.go.jp

• Justin McCurry is the Guardian's Tokyo correspondent