I spent some time last night searching hotels around airports, the criteria being
a moderate walk with bags, no rental car. Now I know why the natives have not been offering suggestions. It seems there are very few mid-Florida public airports with a hotel on site.
Sarasota has a Hilton Gardens across from Dolphin Aviation. There's a Holiday Inn and a Hampton on the perimeter, but on the opposite side of the airport.
Whitted has a Hilton 3 blocks up the street.
Boca has the most convenient hotel, a Fairfield midway between the two FBOs.
Last, Winter Haven has what looks like an old dumpy place on the north airport perimeter.
Oops, almost forgot River Ranch, the dude ranch resort.
The most common lodging at Florida airports? Hands down, it's the county jail or the animal shelter
All things considered, a fly-out to a hotel doesn't look so practical after all. For the price of a Hilton, some fuel, and FBO fees, I can just commute back to 08A and sleep in my own bed.