Bicycle are still important short range transportation for Tokyo residents. So there are many bike shops in this city from small local bike shop to large super-market. But if you look for road bike, MTB, or cross, you need to visit shops called "sports bike shop" or "bicyle pro-shop".
Here is a small list of bike shops for cyclist.
CycleTokyo's Bike Shop Map in Tokyo
http://goo.gl/DcbV9
Y's Road
http://www.ysroad.net/
Y's is the one of biggest sports bike shop chain in Kanto area. They have 19 branches in Tokyo. They stock many road, mtb, cross, bmx, and folding bikes in their shops.
Narushima Friend
http://www.nalsimafrend.jp/cgi-bin/cms/index.cgi
Narushima is a unique bike shop, known as roadies nest. They stock many fancy parts for road bike, including latest Record or DuraAce.
Friend Shokai
http://www.friendsyokai.co.jp/index.htm
The shop was founded in 1933, and has been known as high quality bike shop. They have wide range of stock bike of road, mtb, cross, and folding.
Carnival
http://www.carnivaltokyo.com/
In last 5 years, the fixed-gear bike, or fixie, has became popular in Tokyo. Carnival is one of fixie dedicated bike shop.
Loro
http://www.loro.co.jp/
This unique shop focused on recumbent and folding bikes started their buisiness at Osaka on 1999. They now has 2 branches in Tokyo.
Cycly
http://www.cycly.co.jp/
Cycly is the well organized second hand bike shop chain. The prices are not super-cheap, but the quarity of their bikes are nice.
maki