Before anything, you'll have to learn about the Rivalry between the FSU Seminoles and the Florida Gators (University of Florida in Gainesville). We have one of those mixed families, so Thanksgiving (when the two teams usually play) is an interesting family gathering....
I was a transplanted Gator living in Tallahassee for several years. I had a Gator license plate, even, and I got out alive. Still have family there.
If you bike (bicycle), there's a good rails-to-trails bike trail south of the city that goes down to St. Marks where you can stop and have oysters and smoked mullet spread at Posey's - a very "colorful" place (don't be intimidated by the Harleys out front) - and check out the St. Mark's lighthouse...
Meanwhile, you're not far from the best beaches in Florida - Alligator Point, St. George Island, Destin, Greyton Beach (a tiny town between two state parks that are on the beach... really cute place), Cape San Blas (a must - at the end of the Cape is a state park - camp on the beach! wonderful wonderful) - Panama City beach, etc....
I didn't do a lot of diving while I was in Tallahasee, but Destin is a popular spot for diving. I went there once with a friend when she was certified. If you look at map of the topography of the ocean floor around Florida, you'll see that the continental shelf extends out pretty far - that means there's a lot of sandy bottom. Mostly you'll find man-made reefs to dive on.
Welcome to Florida, from a true Florida cracker. Hope you are happy in your new home.