As a someone who cycles in Tokyo nearly every day, I will add my five cents too.
A single general rule for cyclists in Tokyo is to remember that bicycle is a vehicle, not a pedestrian on wheels. Tokyo is not particularly bicycle-friendly, because of the lacking bicycle infrastructure, but otherwise cycling in Tokyo is fun.
Which means never cycle on sidewalks. It is not only dangerous but also illegal. To give more details - it is illegal if the sidewalk is narrower than three meters if I remember correctly but it would not stop policemen from approaching you if it is little wider.
Second, most cyclists in Tokyo are guilty of paying very little attention to rules so looking at others and doing the same is very bad idea. Cycle only on the left side, stop at red lights, do not cross large road crossings diagonally, do it by same rules as light motorbikes do. And remember that other cyclists often ignore lights and sometimes ride on the right - so have to watch out for them.
Car drivers are usually considerate and other pedestrians should not bother you if you don't ride on the pavement.
Parking is a problem. In most of Tokyo central part parking somewhere on the side of the road is illegal, but you will notice that many cyclists park there. In fact, there's not much choice. Dedicated bicycle parkings are in short supply and unless you leave your bike parked on the wrong place for a very long time it is no problem.