Most of the cave diving sites in the panhandle will require a boat to get to. Jackson Blue is really the only spring you can drive up to. You can get a semi in there but turning around might be an issue. There's a small parking lot at the bottom of a hill and the rest of the parking is typically done on the grass. If it's been raining you'll just get your semi stuck most likely. There are other caves to dive in the area, but like I said, you'll need a boat. There are a few on Merritt's Mill Pond and several on the Chipola River. However, if you are backmount the river caves aren't going to work for you.
Florida Caverns State Parks has camping and they have RV pull-ins so you shouldn't have an issue with a semi. Arrowhead is another option and is mainly for RVers so that should also work.
There are also some caves west of Marianna and south of Tallahassee, but most are river access only or require you go with someone who knows how to get to them.
If you have any more questions give me a call - 850-272-7484. I have a full selection of rental tanks and easy to get fills.