Shinjuku is where I stayed. Within walking distance you have access to a ton of excellent choices (fairly high end and local).
Suggest you stay somewhere very close to any subway entrance. Shinjuku station is a major hub, so it could be a bit noisy, but it is also the center of everything, so west side or east side is fine. Or one station over, Shinjuku san chome area, is fine too.
If you are visiting department stores and want to focus on food in the basement, Shinjuku Isetan and Shinjuku Takashimaya (about 10 ish mins walk from another) are unbeatable. I want to say Isetan's sashimi/seafood selection is a notch better but worth comparing before you buy. The sashimi section is usually in a separate area or within the supermarket. You will find a lot of delectables that you can purchase (and bring back to eat at AirBnB), usually they charge per 100 grams. Then pick up a favorite bottle of wine, liquor, or sake (a ton to choose from, pick ones if you can, that are not exported to the USA) and you will have a blast. Oh, and that bottle of sake in the USA, will cost you half the price over there at the bare minimum (we enjoyed a $100 bottle that retails for $425 to $575 in California, marked up to $1100 at high end restaurants in LA/NY).
For lunch, check out Kappo Nakajima in Shinjuku (they have or previously had a Michelin star, but no need to go there for dinner). For about 700 or 800 ish yen per, and the lunch sets are entirely based on Japanese sardines (iwashi) and come with rice, soup, and pickles. Sashimi (with seaweed, shiso, and sesame seeds), fried, simmered/stewed in soy sauce, or yanagawa nabe (fried with egg, then served in a hotpot with a sukiyaki style broth). The portions are a touch small, but designed to be adequate, and you can get a refill on rice. You can also order the other items a la carte. They have a separate picture menu in English. Go before they open, as the lines form up the stairs from the entrance below. The fried sardines are outstanding.
Second Goryukubo (bookable through GoVoyagin, or ask your AirBnB host) as a kaiseki choice for Tokyo, very likely it will be counter seating. Splurge on the pricier menu and get superior grade seafood (granted you are reaching almost Saison level pricing, but it's a unique experience), else the standard menu is already very good. The hostess (wearing kimono) lived in SF Bay Area for 20 years and speaks fluent English. Great humble selection of sake, she can help recommend (get small carafes if you want to try a variety) though it helps if you can communicate your preferences. They have some wine/champagne as well if you prefer that.