Navigating streets in Tokyo can be very difficult. Sinage is not what I would call intuitive, nor are the way the streets are layed out. The tall buildings affect your ability to orient yourself by visible landmarks. And of course Tokyo is a very bustling town so for me I would be afraid to be on a bicycle.
If you are not already familiar with Tokyo, I would not recommend trying to navigate it on bicycles on your own.
There are however, guided bike tours that you can join. They are even conducted in English if that is your native language.
I suggest searching the web for "Guided Bicycle Tours in Tokyo".
The maps don't have street names because most of the streets don't HAVE names. Find a bilingual map. When you get lost--and you will--just flag down a passerby and point to the bilingual map, say where you want to go, and they'll point you in the right direction. I have a nice little book of Tokyo maps that I got on amazon that was very helpful.
Seriously, do not attempt to bike in Tokyo. Between the incredible density and the fact that they drive on the left, this could be very dangerous. Walk and take trains.