One of the lunches we had in Tokyo was at Yoshitomo Nara’s A to Z Café. I’m quite sure you have come across some of his works, mostly revolving around a sulky looking girl. If you are a big fan of his art, you definitely should visit, as there is a little room in the middle of the café, which you can peer inside and get a glimpse of his art and supposed working space.
If you go at lunch, they only have sets available. When I was there, I was given a choice of chicken or fish. It cost a very reasonable 1000 yen, and in addition to your choice, there were some pickles, a few pieces of sashimi, a bowl of soup, rice, and a cup of tea. The food was light, clean, and had a homely feel to it. Worth a return visit if I ever head back to Tokyo!
A to Z Cafe
5F, 5-8-3, Equbo Building, Minami-Aoyama, Tokyo, Japan