Dear laic
No problem whatsoever
Dear qintana
There is a gym near our hotel, nicely equipped if your into serious training and reasonably priced. Not much else around except in the Korintia hotel but the facilities there are extremely expensive.
As for renting something: I suggest to think twice about it as there is not really any nice area in Tripolis and you will be lost trying to get anything done. Stay in the hotels, at least they take good care of you.