This 120 year old lighthouse sits on a wildlife refuge. The lighthouse itself is not open to the public, but you can snap some nice photos from the outside.
The Sanibel Lighthouse is at the eastern end of Periwinkle Way (and the eastern tip of the island) - just follow Periwinkle to its end, and you'll be in the parking lot for the lighthouse.
You'll need to pay $2 per hour to park in the lot.