Oedo onsen in Odaiba is a great place to go on a rainy day. They have re-created an old, traditional village from the Edo period. It's really interesting. You can even choose the style of yukata to wear as you walk around.
I.T. developer, 30
On a rainy day, I recommend a spot of shopping in Akihabara. I work in the IT industry and I'm interested in computers and video games. There is so much to see and do in Akihabara if you have a similar interest.
Canyoning guide, 2628
People should go canyoning and white water rafting if it's raining. On a rainy day you are going to get wet anyway so you may as well do something exciting. Minakami and Gunma are good places to do this kind of stuff.
I.T. consulting, 35
Rainy days should definitely be spent French-style. This means staying at home with your lover. After a nice, late brunch, you should just go back to bed and lie together for the rest of the day. We call this "siesta."
I always go to the library when it rains. I love the sound of the rain falling on the windows, it's very relaxing. Its a great place to enjoy air conditioning when it's hot and humid. I recommend Gaeiyen Library near Omotesando.
I have a young baby, so I recommend going to one of the children's halls where the kids can run around a bit. Jungle gyms, large play areas and music rooms will keep them entertained. There are public-funded places around Tokyo.