We hit Florida once a year for a vacation with the boys (ages 8 and 10) and we never do the Disney theme parks. Too $$. We do go to the water parks and Downtown Disney to walk around and check out the sights.
One year we went for a drive to the Canaveral National Seashore and wandered around there for most of the day. Took a picnic and stopped at various places to check out the wildlife. We saw some beautiful manatees, neat crabs, a couple alligators and lots of crabs and colourful birds.
There may be a shuttle launch depending on the weather (scheduled for April 5+ on their site now).
There's Big Tree Park
that features a 3500 yr old Bald Cypress.
If you're heading towards Tampa I'd check out Fort DeSoto park
- great beaches. And head over the Sunshine Skyway bridge
- we always get a kick out of it.