Setagaya Ward has about 12 courts for you to use
Setagaya Ward (nearest station would be Sangenjaya and then take the Setagaya line) is a good place to play tennis. Since these are community courts, you need to register in advance at the Setagaya Ward office. If you are going to be in Japan for a little longer than a short visit, it would be really fun to head down to the Setagaya ward office and sign yourself up...they also have other sports you can participate in like basketball, table tennis, etc.
Here is the link to Tennis facilities in Setagaya
For the community courts you would need to be a resident of the ward or have a friend who is one or you could go to the Tennis Center above the Shinagawa Prince Hotel. Here is the link: http://www.princehotels.com/en/shinagawa/tennisgolf