Places to Play: Hotel New Otani (Akasaka)
 
Between the original Hotel New Otani and the Otani office tower is a 5-story connecting building which also extends out to the street leading to Akasaka-mitsuke.  Several tennis courts are on the roof of this connecting building, alongside the street.

The courts were part of a private club when I checked several years ago.   Membership to the club was by invitation.  Given Japan's economic difficulties, maybe this club has loosened its admittance procedures lately.  If anyone gets further info, let me know.