Tokyo Midtown is an modern and fancy complex with lots of different restaurants, shops, museums, a small park, and hotel/monthly apartments. You can get there by subway, just follow the Tokyo Midtown signs from Roppongi Station (Toei Oedo Line or Hibiya Line).
This is a great place to meet with, for example, Japanese business partners. I've been to just two restaurants/bars there, but can recommend both of them:
- Salon Bar Yol (http://y-o-l.jp/), open 17-29 (?) --> I suppose it means until 9 am. It was pretty quiet when I was there at 6 pm
- A971 (http://www.a971.com/), bar 1F, dining 2F, gets quite busy right after work
The restaurants usually have English menus and the staff speak English, at least enough to take reservation and orders. ;-)