I'm specifically looking for neighborhoods with distinct and unique character and not so much the megadistricts like Shibuya or Akihabara.
From a previous question, I've put Koenji, Shimokitazawa and Nakameguro on the radar, but I'd love to know if you have a favorite little neighborhood that you love to get lost in and why.
Daikanyama Station is nice in terms of good shops, restaurants, secluded streets and interesting architecture.
I like Jimbocho. It's still in the city, but there's just a bunch of fun stuff there. I found a bunch of guitar shops ... being a musician, I had an incredible time. I saw things that I'd never seen in-person anywhere else before.
Tokyo is like a big city containing many small cities having their own distinct culture. My favourite place to hang around is Roppongi Hills, Omotesando. If you really want to go totally off track there is Okegawa where you enjoy rural Tokyo.
If you want something hybrid where you get everything but don't want to be in middle of big tourist zone Aoyama
Mentioned in this answer:
I have never been there, but Yanaka Ginza (Market) looks like a nice place to go. This neighborhood is on my wish list.