im going to suggest a 2 stop trip with paddling at both stops. The Rainbow River in Donnellon Fl, is an incredible paddle/float down a spring fed River. The water is carribean clear, we stumbled on it last year during spring break, and we are hoping to head back again this year. Also George Island State park in Fl, the island is beautiful, and you can paddle all through the bay.
Both areas are not real touristy, and a full week might be a bit long for the kids at one location, but both are fun for a few days. It might be pushing the distance, but Google rainbow River, it's even better than the pictures.