J.C.
I'd vote for Cincinnati. The weather should still be pleasant, and there is a ton of things to do there.
The Children's Museum is excellent. The Newport Aquarium (across the Ohio River) is wonderful. The Hamilton Co. parks are awesome and the children would love them. King's Island will still be open on the weekends and they have lots of kiddie rides.
We try to get down there every year for at least a few days. We always stay at a hotel with an indoor pool so the kids can swim. If you were thinking more along the lines of camping, there are wonderful campsites in the area, also. I recommend you get online and Goodsearch Cincinnati.
Have fun!