This is a huge membership club right there in Aoyama. It ranks in quality with the Tokyo Lawn Tennis Club and the Tamagawa-en Racquet Club.
The club has over 20 courts, has a nice clubhouse, is conveniently located ... the only problem is that membership takes years (the last time I checked, which admittedly was some time ago). One unconfirmed report I heard said the route to membership requires first taking one of the few weekday member slots that occasionally come open, then in a few years get "promoted" to full membership able to play on weekends. An interesting contrast with the Tokyo Lawn Tennis Club, which is required by its charter to take non-Japanese members and into which non-Japanese will generally be admitted in weeks.
The club also operates 9 indoor courts next door, and these are available for rental from 3 PM to 11 PM (see the Jingu Gaien Indoor listing for details).
The club requires whites for your tennis pants or skirt. Your sweater or jumper can have color but your shirt or blouse must be mostly white. The shop in the clubhouse sells whites (at designer prices) if you forget and come more colorful than permitted.
Directions: let's use Aoyama Itchome intersection as a starting point (this is also a stop on the Ginza subway line). Go about 300 meters along Aoyama Doori towards Shibuya. You'll come to a large T intersection with the base of the T being a tree-lined boulevard leading off to your right. Turn right onto this boulevard. About 150 meters from the T intersection, on the left side, is a very large round-roofed building which has a parking lot on the first floor and the indoor courts on the second floor. Turn left at the short road just beyond this building. The clubhouse entrance is on the right side of this short road, about halfway to the end.
Coming by foot, bicycle or taxi is recommended since parking is tough in this area on weekends. The parking lot is the first floor of the indoor courts building, with typical Tokyo parking fees. The lot fills up quickly.
The address is Kita-Aoyama 2-1-15 and phone is 3401 0389.