I passed some of that way last summer, in August. Joined the route at Schaffhausen
The first campsite was at a little place called WAGENHAUSEN next to the river Rhein. It was the first bit of socializing with other cycle tourers, as the small campsite had a patch for cycle campers, and a common room where everyone could go when it rained (which it did !)
GPS: N 47 39.774 E 8 50.564 (degrees decimal minutes)
The other site I stopped at was near ALTENRHEIN right on the cycle route 2, the Rhein Route. So more cycle campers and bigger site with more facilities. Again it rained heavily so my memories of it are of taking shelter in the camp cafe, eating pastries and waiting a couple of days for the rain to stop !
GPS: N 47 29.442 E 9 33.931
That was in August 2011, and there had been unusually heavy rain and thunder storms, but when it cleared it was a gorgeous place to cycle.
I am sure you will love it.