Decide what you want from Tokyo, then pick the district which has it. Tokyo is old-school. They have a nightlife district, a financial district, a red-light district, a street that only sells restaurant supplies and so on.
Most of what I want is in Roppongi (but I wouldn't pick this area because this is where foreigners typically go), Kappabashi Street, Ginza, or Shibuya. That's where the restaurants and restaurant-supplies can be found. No matter where I go, I'm going to find a way to the Tsukiji market, which is basically Mecca for me.
I'll bet half the people who go there secretly want to explore Shinjuko -- for the giant Godzilla head that if you frame it right, looks like Godzilla is on the next block. ;-) Just keep in mind that the accommodations in Shinjuko usually rent for a few hours at a time.