Well you can try just about any state park. Ceaser creek would work, and the roads around there are not too heavily traveled. Buck creek would be another.
You could try Eastwood metro park in Dayton, but I don't know if they have a swim beach there or not. Any place there is a beach you could likely do it. The major issue is finding the bike route that is fairly light in traffic.
To bike, you can hop on the bike path that runs from Springfield to Cincy..I plan on hitting it in August when I'm up for a few weeks...I used to live in Yellow Springs, so that's where I know to pick it up-it's a rails to trails path..not sure about bodies of water near it though.