Best spot to bird in the island is obviously the JN Ding Darking NWR, the loop road will give you a good variety of birds depending on the time of the year with guaranteed chances to see Roseate Spoonbills, Reddish Egret, Yellow-crowned Night-Heron and Mottled Duck along with many of the common waders and wintering birds like American White Pelican, Bald Eagle and dozens of shorebird species. If you get a place with beach access, keep a lookout for Black Skimmers, plovers and other shorebirds that prefer beach habitat over the mangrove marshes of the refuge. Surprisingly, Pileated Woodpecker is as, if not more, common than the Red-bellied Woodpecker on the island, so you'll have plenty to see.
Going outside of the island can give you access to more habitats, including the Cape Coral Public Library which is great for Burrowing Owl (Florida ssp.), and an hour drive North or South will take you to Babcock Webb WMA (Red-cockaded Woodpecker, Bachman's Sparrow, Brown-headed Nuthatch, etc.) or to Corkscrew Swamp Sanctuary (Barred Owl, Wood Stork, Painted & Indigo Buntings.).
There are other places to see and check out, but if you want to give just a few places the focus, I'd say to give those priority due to both their popularity and the habitat variety will mean you'll get a good trip list.
