Many gyms in Japan require membership, and the fees for registering are usually quite high. Some gyms however, offer try-out passes for only one day, or let you pay on a pay-per-visit basis. Note that most gyms require a some sort of ID.
There are numerous chains of fitness gyms around Japan. Gold’s Gym offers a ‘visitor’ admission, 2500 yen for 5 hours of training, or a 2-week trial admission for, as the name suggests, 2 weeks of training or 6000 yen (only for first-timers). Here (in Japanese) you can find the locations of their gyms.
Tipness is another famous chain in the country. The all-encompassing facilities are perfect if you want to try out a lesson of, for instance, yoga together with your workout. This month (aug 2014) they run a campaign of trial admissions: once for 1620 yen, three times for 2160 yen or two weeks for 3240 yen. You can make use of this promotion with up to two people (for the same price). Check it out here (in Japanese).
Another option are the public facilities. Every ward has one, so you never have to travel far. The facilities might be a bit dustier than the private fitness clubs’, but that’s reflected in the admission price: you won’t find a cheaper place in the city. Prices range from 200 to about 500 yen, but keep in mind that you often have to prove that you live, work or study in the ward of the gym visited by showing something like a municipal registration card.
Koto ku: http://www.city.koto.lg.jp/language/lang-eng/faci0002.html
Minato ku: http://www.minatoku-sports.com/guidance/index.html (in Japanese)