You need not be a club member to use the courts under lights at night. Just call up and make a reservation, and pay the charge.
The club has 2 doubles courts with artificial lawn, 1 doubles hard court, and 1 indoor hard court. You can play soon after rain. The clubhouse is modest but sufficient -- lockers, showers (for the men, anyway), lounge area.
You can readily become a member of the club. The 99%-Japanese membership is quite friendly and approachable. You'll be able to practice your Japanese language at this club, since foreigners are scarce. While a member there, I found that I could play 3 to 4 sets of singles if I arrived at 8 AM on a Saturday morning.
Regular-membership fees are 150,000 yen for one year, 550,000 yen for five years, plus monthly dues of 7,000 yen per month. There are cheaper membership categories for weekday-only play.
To get to the club, from Naka-Meguro station go north towards Ikejiri-Ohashi on Yamate Doori about 600 meters to Aobadai 1-chome intersection. Turn left, go up the long slope about 600 meters to the third traffic light. Turn left again onto a narrow road and a sharp downslope. About 50 meters in on the left side is the entrance and parking lot to the club. Telephone is 3711-4551 (Japanese is best); address is Kami-Meguro 5-12-20, Meguro-ku.