Places to play: Shinagawa Prince Hotel
The Shinagawa Prince Hotel has 9 indoor courts with artificial lawn, basically available in a first-come first-serve basis. Weekend and evening times are the hardest to get, while early morning hours are much more available. The place is open 24 hours a day on Thursdays, Fridays and the day before a holiday, and 6 AM to 2 AM otherwise, so "early morning" can be as early as your body and brain can stand. Rates reflect good ol' capitalist supply/demand: cheapest is 7,000 yen per court per hour from midnight to 9 AM on weekdays, going up to 14,000 yen per court per hour for 9 AM to 10 PM on weekends and 6 PM to 10 PM on weekdays. Two of the courts are "private" i.e. enclosed apart from the others, and have a rate structure a few thousand yen higher than the above. There's no airconditioning, but lots of opened windows/vents in this huge prefab building. Friends have debated the gain of shade from hot summer sunshine against the loss of any cooling breeze. Lessons are available at 5,000 yen for 50 minutes; the coaches have limited ability in English. Reservations can be made at 3441-0020 or 3441-0090 from 9 AM to 7 PM. Cancellations 3 days prior are at no charge; charges thereafter.
Getting there: The Shinagawa Prince Hotel complex is right across the street from the JR Shinagawa Station. The huge tennis building is on the back side of the complex, all the way up the slope. By train: From the station, directly across the street you'll see a MacDonald's on the corner. Go past MacDonald's into the pathway behind the buildings facing the Pacific Hotel, and towards the bowling alley of the complex. Follow the pathway past the bowling alley all the way up, about 300 meters.
By car, from the Roppongi/Azabu area: Take Sakurada Dori (Route 1) south. At any intersection soon after passing Meguro Dori, turn left to move over to the two-lane road that parallels Sakurada-Dori. Continue south. As you pass the Shin-Takanawa Prince Hotel on your left, you'll come to a corner where if you turned left you'll go down a slope and end up right at Shinagawa Station. DON'T turn left to the station; instead go straight ahead into the slightly narrower road. The huge tennis building is about 100 meters in from this corner, on your left. For parking (charged), turn in left just before the building.