I was wondering why everyone was talking about Ft. Myers, which is quite a haul from TV. I believe the OP was talking about Pine Island in Hernando County that's only about an hour and half from here.
I use to live in Spring Hill and Pine Island was the only beach we had locally, although you have to go out a few miles from Spring Hill. I haven't been there since 1989, but I remember it as a state park and had public restrooms and picnic areas but no real businesses.
If you want more of the tour attractions along with the beach, head to St. Petersburg Beach or Clearwater Beach, I think the Gulf Coast has the nicest beaches. That's probably a two hour drive down I-75 to I-275. If you want something just a little closer I would try New Smyrna Beach on the Atlantic, but I don't believe it's quite as nice.
Here's the Pine Island in Hernando County, take Route 50 from I-75 and just keep going west, when you cross US 19 you're getting close.
