Gonpachi
Gonpachi is known Izakaya as the former Prime minister Junichiro Koizumi went there with the president of America, George W. Bush when he visited Japan.
They serve excellent Yakitori ( grilled chicken on sticks), Soba (buck wheat noodle) and homemade Japanese food with reasonable price in the Japanese traditional surroundings with the paper lanterns.
Some of the staff speak English. Reservation are recommended.
How to get there from Oak hotel.
Take Ginza line from Inaricho subway station to Tameike-sanno station. Then transfer Yoyogi line to Nogizaka station.
See the website below, more details are here
http://www.gonpachi.jp/jp/nishi_azabu/home/location