The best restaurant I've been to in Tokyo is Kaikaya (開花屋) in Shibuya. It's not far from the famous department store Shibuya 109, but is tucked into a small street abouta ten minute walk from the train. See the map on http://www.kaikaya.com/
They have excellent fish and beef dishes, especially "maguro no kama no Supearibu" (tuna spareribs --- amazing!) and "shimofuri kobe-gyu no nigiri-zushi" (wagyu beef sushi).
The ginger beer (non-alcoholic) was outstanding, and they had a very large selection of unusual sake and beers. The menu is very seasonal and all of the ingredients are fresh so sometimes certain items are not available from day to day. The owners and staff are very friendly, and while very little English is spoken the menu is translated into English, so you'll be alright if you don't know any Japanese. You just need to find the place first! By Tokyo standards it is not even very expensive.