Pierre,
We spend most of March on Sanibel Island every year. The place is very rustic, no traffic lights, no MickyD's, no buildings above 3 stories, lots of wet land preserves and bike paths to everywhere.
There was an airport on the island years ago but it is long gone. The only way to get there is to rent a car from Page Field. It would be a nice day trip across the cause-way ($6 round trip) with a stop at the Ding Darling Wild Life Refuge and a guided tram ride through the refuge ($8 each) and then on up to Captiva for lunch at maybe the Bubble Room, the Green Flash or the Mucky Duck. (Captiva has 2 classes of people, the millionaires who own the property and tourists who visit along with hired help that commutes from off island. Normal people do not live there. Sanibel is somewhat exclusive in that regard but not like Captiva)
My take on the rest of Southwest Florida is too many people, too many cars and inadequate roads to handle the mass of humanity. About the only worthwhile thing to see in all this congestion is the Edison-Ford museum in Fr. Myers. It would take a couple days to do it and Sanibel.
(There is an island airport north of Sanibel on what may be called North Captiva but I do believe it is private. It is an east-west strip (seems to me grass) with water not far from either end. I saw a Cherokee there once when we took a boat tour out of Captiva to Boca Grande)
Sounds like an interesting trip. We've done Key West from Sanibel and took a "city" tour which was most interesting. (I flew out of the keys at night years ago with a single engine and wouldn't do that again, it is mighty, mighty dark until you get past the Everglades.)
PS At the very least, fly over Sanibel from the cause-way and up the beaches to Captiva. Pilots do it everyday. Commercial traffic into Regional Southwest over fly the coast and appears to be at about 5000'. There is an airplane ride operation out of Page flying a Waco or Stearman up and down the beaches most every day. It easy to fall in love with Sanibel...Turbo's take on the island is not quite right....it is not like Fr. Myers Beach in any way....and there are no airports on the island.