Thrylos98's Fort Myers Culinary Guide has some excellent suggestions. I would particularly endorse the Prawnbroker on McGregor -- excellent seafood at a very reasonable price. A hint that it's good is that the place is regularly packed with locals. University Grill, owned by the same company, is also good with a slightly different menu and more of an upscale saloon ambience.
If you don't mind a short drive, some of the best dining is found over on Sanibel Island -- I recommend Doc Ford's, Matzaluna for homestyle Italian and the Island Cow, which has quality food even though it has every imaginable dish known to mankind on the menu. Also on Sanibel, a little off the tourist path, is the Beachview Golf Club restaurant, a nice steak and seafood place that has German Night every Wednesday.