How's your Japanese? You'll need to know a bit of it in order to get around effectively. Also, it helps to have a Suica card to get around the JREast and Metro lines.

W-Base Harajuku is a good stopping point if you happen to be near Shibuya and you're into fixed gear or BMX. You'd have to either walk several blocks north from Shibuya-eki or a few blocks south from Harajuku-eki on the Yamanote line. Also in Shibuya is BlueLug, which caters to the fatbike crowd (getting more popular, supposedly) and Carnival (more fixedgear) across Yoyogi Park.

Y's Road in Akasaka is the bigbox bike superstore, if you're into high-tech stuff (such as late-model Anchor/Bridgestone road machines). There's another store just south of Ueno / north of Akihabara, right on Chuo-dori. Ueno-okachima station is the departure point off of the Yamanote-line for the latter, or you can get off at the Electric Town exit at Akihabara-station, then walk west-then-north on Chuo-dori and watch Akiba get its freak on (Sunday is weird day). Yodobashi Camera just build a superstore next to Akiba station, which has a fairly large selection of mamachari bikes and good ramen restaurants on the top floor.

Punch Cycle Asakusa is probably your best bet for vintage Nihon jitensha iron. You can get to it from Tawaramachi station on the Tokyo Metro (not sure what the line is, though).

Cherubim is someplace near Roppongi, I think. They decided not to post their address on the website, though I heard they give tours.

I recommend Ramen Jiro in Ikebukuro. Just be aware - for your 1000 yen you're going to have to consume a monster bowl in about 15 minutes, while hungry kanto-jin watch and wait impatiently for you to finish. Also fun is Anna Miller's in Shinagawa (Wing Takana Mall 2nd floor) or Hiro-o. Get the Fruits Cream pie and the coffee.