They lease the launch pads, e.g. 39a has a 20 year lease. They can probably do a lot of spacey things on there for the duration.

https://www.nbcnews.com/science/space/spacex-signs-20-year-l...

edit: looking at the article map, this is patch of farmland a bit further away from the launch pad, so they probably acquired it for development.

In addition to paying rent on the land, SpaceX pays KSC/CCAFS/the Air Force for launch services support.

They pay range fees, but may not pay much for the facilities themselves. It's not uncommon in things like this for the lease to be offset by the improvements built or simply for taking maintenance of the government's hands.