The Japanese have a tradition of communal bathing in public baths, and these are still very popular today. Many of them use water from natural hot springs. If you have the time you can take a trip to a hot springs resort, but if you can't make the trip then you can still try out the baths in Tokyo.
There are a number of onsen baths (fed by hot-spring water) in Tokyo, I visited a small one in Asakusa, ask at your hotel and they should be ble to direct you to one nearby.
The procedure is simple enough; you leave your clothes in a locker and head into the shower room where you wash yourself thoroughly before getting into the baths. There are pools of varying heats, including a cold plunge pool which you finish up in.
It's very relaxing and the perfect way to sooth your tired muscles after a hard-day's sight-seeing.
Bring a towel, soap, shampoo, etc. though you can usually buy these at the baths. You might also want to bring flip flops or something, of course you have to remove your outdoor shoes as you come in...