新宿 Resturant for Dinner.

There are lots of good places for dining in Shinjuku (新宿). Followings are some of my recommendations:

(1) 瀨里奈(和牛) http://www.seryna.co.jp/shop/shinjyuku.html
Famous Japanese Steak (wagyu beef) restaurant with good view. Dinner should be out of your budget, but you'll be able to enjoy famous wagyu beef lunch set at only around 3000Yen.

(2) 網八(天婦羅) http://www.tunahachi.co.jp/
Famous tempura restaurant. You may order a la carte, or dinner set with tofu, seafood tempura etc:
http://www.tunahachi.co.jp/news/kisetu.htm

(3) 築地玉壽司(壽司) http://r.gnavi.co.jp/g203823/
A sushi restaurant that is convenient located at Takashimaya Time Square. You may order a la carte, or the sushi buffet at around 3000yen per person.

(4) 鳥良(豆腐) http://www.samukawa.co.jp/toriyoshi/shop/shinjuku/index.html
A decent restaurant that is specialized in Japanese style chicken wings and tofu.

(5) 蟹道樂(蟹) http://www.douraku.co.jp/kanto/
Perhaps this restaurant will be out of your budget, but this is a famous place to enjoy Japanese crab.

(6) 鳥元(居酒屋) http://www.ramla.net/
Places where typical Japanese guy can enjoy drinks with food. Could be smoky.

Hope it helps!