I am a big fan of Marriott hotels and it looks like they have all the usual suspects (Springhill Suites, Courtyard, Residence, etc). Same with Hilton properties (Hilton Garden Inn is a nice one).

If you like small boutique hotels, this one looks promising (Indigo branded hotels are a new part of the Holiday Inn family)

http://www.tripadvisor.com/Hotel_Review-g34230-d1026528-Reviews-Hotel_Indigo_Fort_Myers_River_District-Fort_Myers_Florida.html

Its in town (which cant be too far from the airport) and gets high marks all around.