Not sure how close you want to be to Tampa but I can suggest a couple of good parks.  Our number one pick for that area is Fort Desoto Campground in Tiera Verde, just south of St. Pete. It's a very popular campground so it may be tough to get a site but it has the best sunsets over the Gulf, especially if you can get a site right on the water.  When we stayed there a couple of years ago we talked to a workamping couple who got the job just by being in the right place and asking about it. It's run by Pinellas County.

Another favorite of ours when we visit the Florida RV Supershow is Hillsboro River State Park.  It's a little out of Tampa near Thonotosassa, kind of northeast of Tampa.

South of Tampa we've stayed both at Myakka River State Park and Oscar Scherer State Park.  Myakka is famous for its BIG gators.  They have an airboat ride you can take that looks like a steamboat and gives you an up-close-and-personal look at some huge gators.  Oscar Shearer is in Osprey, just south of Sarasota.  It's heavily wooded yet close to the beach.  There are lots of activities in the area to keep you busy.

I can't comment on any workamping positions but if you're looking for a volunteer position at a state park for winter 2014, you may be too late by waiting until March 2013.  We secured our position for this upcoming 2013 winter season last year around Christmas time! It wouldn't hurt to submit your applications this early for a year and a half away. It also helps to seek out a personal interview with the volunteer coordinator where you want to be. Face to face beats a computer application every time!

Hope this helps!