Here is a list of Japanese railway museums that were known about at the end of 2009.
Also listed are tram and subway museums, museums that feature railways as part of a larger display, and specially operated/preserved railways.
The Tokyo Transportation Museum used to be the first stop on any visit to Japan, but it closed and the railway exhibits were moved to a new out of city museum in 2007.
The same happened to the west of Japan with a new central railway museum which opened 14 March 2011 in Nagoya. Wikipedia on new central railway musuem
There are lots of small railway museums, often with just one or two locos and a few other exhibits, some only open at weekends and festivals, but the bigger museums are definitely worth the visits and are usually open six days or seven days a week (the usual closing day in Japan being Monday). The split between small and medium museums is fairly arbitrary and is based on the size of the railway content.
See page for listing - little information available for most of these
In varous parts of Japan there are regular steam operated services over mainlines. The Japanese Railway Society keeps a list of these.
Around Japan in various city parks, squares, railway station yards, museum yards, and so on, can be seen preserved various plinthed static locomotives. There are too many to list here - keep your eyes open whilst in Japan!