June/July in Florida is HOT – humidity levels are high by this time of year and storms are frequent and intense so camping won't be too comfortable. I imagine it may be the same all the way from here to Indiana, just not as bad further north. Chattanooga is a halfway point for you, so I'd look for camping in and around there. It's sort of tucked into the Blueridge Mountains so it will probably be cooler – it's a very pretty area. Or you could go through Cincinnati to Knoxville, TN, then explore Great Smoky Mountain National Park – there's lots of good camping there and great little towns to check out like Pigeon Forge, Cherokee (North Carolina) and Asheville. A great spot to camp is Mount Pisgah Campgrounds next to the Pisgah Inn on the Blue Ridge Parkway. I've stayed at the inn, but the campground was closed due to bear activity when I was there last summer, so be sure to check conditions ahead of time. (We stayed instead at the Davidson River Campground in Brevard – that was a good spot too).
