Places to play: Shinjuku Hilton
The Shinjuku Hilton Hotel has two courts - one for singles and one for doubles. The surface is a hard surface with a rubberized coating. Wind swirling among the nearby skyscrapers sometimes provides added liveliness to the ball.
Strictly speaking, court usage is for hotel guests. The tennis pro there said corporate and group relationships have been set up (such as with the Tokyo American Club) which also enable non-hotel guest usage. Ask for him at the hotel's general number, 3344-5111, to get his advice on the whats and hows of this. The charge is about 2000 yen per person per hour. He can also give directions to the hotel, which is among the cluster of skyscrapers west of Shinjuku station.
The tennis pro is with PBI (Peter Burwash International). See the page for PBI for more info.