Well you probably won't find a state park site for any lengthy period south of Tampa unless you're willing to go inland further. We've got a reservation for Highland Hammock SP near Sebring in January. You may find something there. It's a nice park, but you're a good long way from either coast.
There are private parks of course, but the ones closest to the Gulf and south of Tampa are either crowded, expensive, or booked. Down in the Arcadia area you will find some further inland, but certainly not as far inland as Sebring. Check out the RV Park Review.com listing for parks in Arcadia below.
We've stayed at Riverside RV Park which is actually quite close to Port Charlotte, but has an Arcadia address. It's nice and has 500 sites, nice pools, plenty of activities, and well taken care of. February will be booked, but January might work. Note: If you're not familiar with Arcadia it's a rural farming town. Some of the parks listed are north of town a ways with a rural atmosphere, but fairly inexpensive for being warmer and well south of I-4.
http://www.rvparkreviews.com/regions/florida/arcadia
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