Diamond members, DO get comped gym useage. One of the nicest views of the city, so you should try it out.
Also there are laser discs in the room and you have a choice of some reasonable entertainment gratis.
Wander around Shinzuku , Omotosando, the Ginza . Most restaurants have English menu's and take credit cards (unlike the taxi's).
One of my alltime favourite hotels. Enjoy.