There are actually quite a few great choices, Cedar Rapids is our home territory. The State park you are thinking of is Lake McBride state park, it is on the Coralville resevoir. The link for it is:
IA DNR: State Parks,Lake Macbride State Park
There are also several COE campgounds on the reservoir, we really like both Sugar Bottom and Sandy Beach and West Overlook is pretty good. Here is the link to those:
Corps Lakes Gateway: Iowa - Coralville Lake
These parks are actually between Cedar Rapids and Iowa City.
Our two favorite parks are actually closer to Cedar Rapids and are Linn county parks. they are:
Morgan Creek: Morgan Creek Park - Linn, IA
Squaw Creek: Squaw Creek Park - Linn, IA
That ought to give you lots of choices, hope you enjoy your time in our area. We will be living in our RV this summer and you may find us in one of these parks, perhaps we will meet along the way.