Places to play:Yoyogi Uehara (Shibuya Ward)
 
Shibuya Ward operates a Sports Center - a cluster of sports facilities, among which are 4 tennis courts, plus 2 courts nearby in the Yoyogi Nishihara Koen (park), run under the same system. Shibuya Ward also has a sports ground along the Tama River, which has 5 courts among other facilities (see Futago Tamagawa /Shibuya Ward info page).

The Sports Center is north of Yoyogi-Uehara station (Odakyu and Chiyoda lines) towards Route 20 and the Keio line, about 12 minutes' walk.   Quite convenient for the cluster of foreigners living in Yoyogi-Uehara / Tomigaya !   The 1,000 yen/hour fee is nice too - if you can get usage through the lottery system. 

Closed on the first and third Mondays of each month (if a holiday, then the following day).

The Sports Center is at Nishihara 1-40-18, Shibuya-ku, and phone is 3468 9051.  Calling in Japanese is best.

LOTTERY SYSTEM

Usage is through a lottery system.  You must live or work in Shibuya ward to be qualified.  My quite dated materials indicate:   Lottery drawings are held on the 2nd and 4th Wednesdays of each month, for the month after next (i.e. drawings in January are for March times).  The drawing for outdoor facilities (= tennis courts) is from 1:30 PM.  You must be present to participate. Attendees are given numbered slips, then numbers are drawn randomly.   The person with the first number gets first choice of a 2-hour time slot first, and so on.