Be sure to wander around the really nice garden behind the New Otani Hotel, which I believe is right across the street from the Akasaka Prince.

The New Otani has a revolving Chinese restaurant at the top that last time I was there served an overpriced (but not terribly so by Tokyo standards) all-you-can-eat dinner. The food was only just OK but it was quite nice to sit at night and watch the city go by. Don't drink too much or you will forget how to find the food, which was on the non-rotating portion of the restaurant.