Railroadtycoon has ventured into the dark side and stopped riding the train (in Central Tokyo) for a bit (yes even in this typhoon weather) and began riding my 折りたたみ自転車　(foldable bicycle), from home to my local station, then I pack it up into the bag, travel into Central Tokyo, where I unpack it and continue traveling about Central Tokyo. Central Tokyo is quite small and it is very much possible to bike from Tokyo Station to Shinjuku Station in a reasonable amount of time, since I've walked that distance before, I also usually cover Shinjuku down to Shibuya via Harajuku as well. But i'm out of shape, and the foldable bike has 16 inch wheels so it can be tiring. If you have the legs it is very much possible to walk it too, which I've done before I got the bike.

I usually use google maps to check out possible routes.

The hard points:
1. Finding a parking space, though often people park in clearly designated "no parking areas", though the "bike patrol" often comes and tows rows and rows of bikes away. In which you have to pay some 3000-5000 yen to get it back from the inpound. Luckily it hasn't happened to me..yet.

2. Biking within the area of the major stations is a pain, because of the large number of pedestrian and vehicular traffic, however once you get a bit from the major station things pretty much open up on the sidewalks/pavements.

3. Taking your bike on the train, since I have a foldable bicycle, and bag, I have no problem, well except in rush hours where it's a pain in the butt to carry around on the crowded trains. However, if you have a full sized bike, the wheels must be taken off, and the bike must be in somesort of cover bag to transport it around on trains. I don't even attempt to take it on the bus, then again, I have a bike so I don't ride the bus anymore.

4. Depending on the area, technically you're supposed to ride on the street with regular traffic, however many people ride on the sidewalk/pavement, and there are some areas where there is shared bike/pedestrian pavement areas.

5. Truthfully, I only do it because it saves me money on my monthly commuter and bus pass, it can be a pain in the butt (literally) sometimes, especially parking, bike parking especially around the stations can be full fast, so you have to find alternative locations, and hopefully it doesn't get impounded away.

6. Police checks, many bikes in Japan are registered to prevent theft, so the Police do occasional bike checks, they usually don't stop me, (maybe I look honest) any case, since you're bike is from overseas and there's no registration plate, just be able to explain that in case you do get stopped for a bike check. Oh yes, at night the only thing the police really care is that you have a front light for night riding. Also standard stuff, no talking on the phone while riding. Also technically you're not supposed to ride the bike while holding an umbrella, though this regulation seems slide through ok without problems.

Edit: Just one more item, for whatever dang reason you can't bike across the Rainbow bridge!!, you're not even allowed to walk with your bike across. I'm not sure why.

The above was for cycling in Tokyo and Kawasaki, I cannot comment for other cities.