That's a tough question. Maybe Shimo-Kitazawa? I have found out about it after 2 years living here from a foreign friend. It really isn't too crowded, and there are many old and new shops, old-style cafes, arty stuff.
To think of it, Komagome and Yanaka Ginza are full of Japanese old ladies, but there are not many tourists. Actually, there are NO tourists in Komagome. It is a really old and sleepy area with old shops, streets, and there are two garderns in the area: Rikugien and Kyu-Furukawa.