There are a couple of state parks in the geographic area you asked about. O'leno State Park south of Lake City is convenient to I-75. It is located on the Santa Fe River, a tributary of the Suwannee, and one of several waterways in Florida that plunge underground for a ways (in this case about three miles) and then re-emerge and continue on their way. It goes underground in the park. It is an older park. I haven't camped there in a long time, and never with a trailer, but I believe it has hookups and adequate space in many sites.
Payne's Prairie State Park is 10-15 miles south of Gainesville near the small town of Micanopy on the south side of Payne's Prairie. I've never been to the campground so not sure about it's arrangements, but also convenient to I-75.
If you have time for a more scenic drive, Manatee Springs State Park near Chiefland might be a possibility. It is on the Suwannee a few miles above where it reaches the Gulf. If you choose this option, you could leave I-10 at the Highway 19 exit below Monticello, FL and follow 19 down to the road that leads to the Park. Then a couple of optional routes to rejoin I-75 at Ocala or below.
I'm not familiar with any of the commercial campgrounds along that stretch.
Paul (in Tallahassee)