You're basically looking for interesting walkable neighbourhoods that are in reasonable proximity from one another so that you can hop in between by bike, correct?
The area that comes to mind immediately would be Shibuya as the base from which there are interesting neighborhood to the south (Daikanyama, Nakameguro), west (Shimokitazawa, Sankenjaya), north (Harajuku) and east (Aoyama). Further down along Toyoko line, you've got Jiyugaoka which great... I am partial to Setagaya-ku and beyond, heading down towards Yokohama.
Unfortunately Jiyugaoka itself lacks great hotel options, and I'm not sure if there are good hotels somewhere between Jiyugaoka and Shibuya. But the advantage of staying around the area between Shibuya and Tamagawa (Tama River) would be that you'll have access to Tamagawa cycling road which goes all the way to near Yokota AFB, in addition to being able to access all the aforementioned neighborhoods even though Shibuya would still be a lot more central.
Futako Tamagawa is an awesome area with a good hotel (Tokyu Excel) and a huge shopping center, although I'm not sure you'd be into that and it is a bit out of the way with respect to those other neighborhoods if you're going to be biking.
If you just want to be able to ride bike but then you are okay with relying on trains to see places, then Tachikawa is a good option. Tachikawa itself has tons of food and shopping, you have easy access to Tamagawa's cycling road, there are many great parks and semi-nature areas nearby, plus you can probably bike to Kichijoji which is an amazing area to explore.