hey whats up man,
when i lived in das Deutschland, I went to a gym called "McFit", it's a nationwide chain. from the link below, there are two gyms in Mannheim.check out which one will be near your residence.
I highly recommend this chain of gyms, they are very nice, new equipment (it was new in the gym i went to in Gottingen and Munich) and most importantly, it's cheap! it's like 19EUR per month (plus another 20EUR, i think, for your card). With your membership, you can use any McFit gym in germany. it's great.
One thing about this gym is that they only do 1 year contracts so if you will only be in Germany for under a year, I suggest you take a valid document clearly showing that your stay will be for under a year. Without this you will be required to get the one-year contract. ALSO, take your passport when you go to sign up. ALSO, if i remember correctly, you have to register yourself to the city before you can sign to the gym (or to anything to be honest).
Do you speak german, btw? when i went to sign up, none of the employees did, so...be prepared! =)
if you have any other questions, message me or something....GOD i miss Germany! =(