There are quite a few public pools in Cedar Rapids, I'll let someone else tell you which ones are the best. There are also a lot of parks - one I like is outside of town called The Palisades. Very pretty area. Heres a link for public pools. (At the top of the page there is a list of the pools with links provided.)
City of Cedar Rapids, Iowa - Department of Recreation
I'm sure there are quite a few fitness clubs, and as earlier I'll let someone else tell you those because I'm not sure - obviously there are going to be a few 24 hr places as in any town such as "Anytime Fitness," etc...
Coral Ridge Mall in IA City has a big play area, I don't remember if Westdale or Lindale in Cedar Rapids had anything like that or not.
There is an awesome waterpark Northwest of Cedar Rapids (about 45 minutes) called "The Lost Island," outside of Waterloo. It's a very clean park with at least 12 slides. They also have very large areas for kids to play.
Lost Island Waterpark