I'm don't know of any campgrounds that meet your requirements.
However, I spent three days riding different sections of the Ohio trail system in the Dayton area based out of a hotel in Xenia. The rates were good (58$), it was centerally located dowtown with trail access less than a 100 yrds away. I found the trails in the area to be nice and certainly enjoyed ridiing into Dayton to see the history of the area.
I've got a retirement goal of riding 100 miles in all 50 states. My wife and I travel in a 15 foot aluminium "toy hauler" type of camper but will splurge for a hotel in some of the urban areas.
If you have any bike travel questions I've have experience and opinions.