Just found out you can, theoretically, hop a train from Brooksville to Clearwater, but by the looks of things, it would probably be quicker and easier to walk.
I know all about those spots out on the coast. Most weekends you can find me and/or my brother out there in our camo'ed up canoe, hunting monster reds and sea trout.
Linda Pedersen(SP) Park is good for an overnight spot if you're sneaky. Stash your gear in the swamp and hit the beach all day, when the park closes walk across the street to Jenkins creek hang out there until about an hour after dark, cross the foot bridge back into LP, grab yur stuff and shack up under one of the pavilions. If you got a tarp, hiding up against the back of the bathrooms is a good spot, you won't be seen in the EXTREMELY unlikely chance somebody patrols the park. Only downside is you gotta be up, packed and have your stuff stashed well before sunup, just in case the workers decided to clean up in the morning instead of the night before... You might also have to fight off raccoons...
Avoid the temptation of sleeping in/under/around the observation tower. Best case scenario, you get run off by a couple looking to get nasty. Worst case scenario you wake up to a couple getting nasty, or you wake up with a used rubber next to your head.
Wouldn't recommend spending too much time in Jenkins creek at night. Lots of creeps out there when the sun is up, even more when the sun goes down...