If you really want privacy, get a private room at a Japanese restaurant (one with a hole in the floor so you don't have to sit cross-legged. Good ones include Inagiku and Seryna. Also, Otabe has well spaced tables as well as semi-private areas for teppanyaki.

Outstanding food (new American/fusion) can be had at March. Since the renovation it is much more spacious and not noisy in any case.