I can tell you up in the Ocala Nat'l Forest you can do much camping...
Silver River State Park
All have tent camping, with electric/water or w/o either i believe. Being in Oviedo, this would probably be a couple hr drive to get to any of these..But they are good camping spots. There's also over by Ormond beach, Tomoca State Park. My family and i went there for a weekend about a month ago..It was fun, clean bathrooms/showers, very family friendly. Ormond beach is a 10min drive away.
If you camp in Ocala National Forest, either stick to one of the spots that ParaCad mentioned, with a full time host, or get off of the beaten path. There are several primitive sites that you can camp at, but there are no staff there to keep things in check, and it can definitely get "interesting".
Blue Springs State Park in Orange City might be another good option, though I have never personally camped there.
Be sure to visit one of the springs in the north central Florida area. Ichetucknee, Manatee, Fanning, etc. are lots of fun, and kids can't get enough of them. I am sure there are springs closer to the National Forest if that's where you'll end up, I just haven't done much exploring in that area.