I used to live in Nagoya and have been to Hamamatsu, Numazu, Shizukoa, etc. for business. Lovely area, the Izu peninsula is superb btw. I am sure you will enjoy it there.
Monthly gym memberships in general pretty much anywhere in Japan are steep unless you can find the exception to the rule (at least in my experience). Depending on your workout needs/ regimen you might be better off buying new/used equipment and putting your own home gym together piecemeal.
That's what I did, and I was able to find some good bargains for less than the costs of a full-year's membership at the local gym in my area. Anyways, not very specific advice I know but just keep your options open and don't sign up at the first gym you find. 8-p