You picked the right time to visit.
A Japanese friend of mine just came back from a visit in December. Even though, you are not looking for them, she said with the value of Yen, Michelin star restaurants were available ~$125 per person.
Cultural speaking, there is drive to improve one's craft or art. Therefore, wherever you go, it's easier to find a certain baseline level that is quite good. Unless you're looking for a one of kind speciality cuisine. We really enjoyed just going to the attractions and walking around and finding little places to try.
My suggestion is just to search when you hungry within that geographic boundary. Again, tabelog, is the easiest way to see what's available. It has google translation tied into the site and reservations so fairly easy to do on the fly.