RSW is the closest airport-- it is ~20 minutes from RSW to downtown Fort Myers, so easily accessed by Uber or taxi. However, it is a smaller airport. For those coming from Canada or farther away in the US who might need more flight options, Tampa (TPA) is approximately 2 hours from downtown Fort Myers, but would then require renting a car.
I highly recommend staying in downtown Fort Myers. From there, the Burroughs home can be accessed easily by walking or the downtown trolley. The hotels we recommend are listed below.
For larger groups, there are some really cute homes on Airbnb and Vrbo for a great price within 2-3 blocks of the venue!