I live in Cincinnati and have visited KI many times, but I've never tried camping there. Your question made me do a search, and boy did I find a lot of OUTDATED
information! There is no 'Paramount Kings Island Campground'
, it's been torn down and replaced by a resort hotel years ago but still shows up on many websites.
State and County Parks
Cowan Lake SP Ohio State parks - Cowan Lake State Park
Winton Woods County Park Hamilton County Park District - It's Great Outdoors! ®
-- very nice park, 19 miles (30 minutes) away.
Cedarbrook Campground Home
- Close to Lebanon, OH, very historic old town. Check out the Golden Lamb Inn.
Olive Branch Campground Olive Branch Campground, in Oregonia, Warren County, Ohio
Beechwood Acres Campground https://beechwoodacres.com/
Morgan's Canoe Rental Canoe Rentals in Ft. Ancient on the Little Miami River in Morrow, Ohio
Great people and great for canoe or kayak trips on the Little Miami River, BUT the camping is no hook ups, mostly tents. Very close to KI.
Buy KI discount tickets at Kroger, Meijer is not selling for 2013, (more wrong internet info) If in the area, visit Fort Ancient SP museum, Cincinnati Zoo, Museum Center, Newport Aquarium.