I'm originally from the area and spend a fair amount of my summer on AMI.

Ride: Easiest ride is a 40 mile roundtrip from Anna Maria to the park at the south end of Lido Key. Pancake flat except for the bridges.

Swim: the closest proper lap pool for public use is near St. Armands Circle in Sarasota I *think*

Run: There are treadmills at the Anna Maria Community Center (some house rentals include membership), I've never run on a treadmill on AMI i just do 4-6 mile loops around the north half of the island, I've done a couple long runs headed south though Holmes Beach just following the sidewalks.

Have a great trip! PM me if you have any other specifc questions.

Lucky you! Enjoy the heat.

The bikes easy, like run robin said, up and down Long Boat Key, pancake flat, but wide shoulders. OWS swim at Lido Beach or at the public pool there for a couple of bucks. Run? good luck in the heat!
M