Just to the North of the Sheraton Miyako is Azabu Juban. It's less than half an hour's walk. It's a charming area well worth exploring, bristling with restaurants with its own fair share of decent clubs and nightlife. At the most, a cab back from here to your hotel will cost 1,000yen. Another 20 minutes walk to the North of Azabu Juban is Roppongi - a more infamous nightlife zone.

Here's a thread I've already compiled about just some of the many dining options around your hotel.
http://www.flyertalk.com/forum/japan...yo-miyako.html