Sounds like you’re into about the same kind of things I’m into.

Here’s what I’d do if I had the time:

Head south along the coast.
Hit the Shell Factory in Port Charlotte
Time it so you can watch the sunset over the Gulf on a clear day
Head east on Alligator alley. See how fast the rental car can go. You can also hit some Indian tourist traps
Hit the East Coast and head south
Cruse all the way down to Key West
On the way they have some sea life stops like a Dolphin petting/swimming place and other attraction
Once in Key West take a snorkeling cruse. I think the best part about Florida is snorkeling around the reef.
Go to sloppy Joe’s and they have a nightly celebration on the Warf.

I’d then take 95 North and head over to the coast right above where you turned south.
If you want to see some unbelievable houses hit the coast around Jupiter
If you have the time I’d head up to Daytona Beach. Driving a car right on the beach just rocks.
Then head over to Cape Kennedy and see the NASA space museum
If you want, hit Lake Okeechobee but that gets a little boring
If you’re into Drag racing hit Don Garlits museum in Ocala. ->www.garlits.com/
I know you said you’re not into the Parks but they really are something to see. And if you stay there stay at one of the Disney hotels. They are nice!