Joking aside, there's an absolute ton of stuff to see and do, that is unconnected to Disney or Universal.
St. Augustine is a very interesting and relaxing day out (located between Jax and Daytona on the Atlantic coast). The mediterranian architecture coupled with spanish moss festooned FL Live Oaks make it atmospheric and 'old America'. I love the place.
Wekiva Springs State Park is also great (as is Silver Springs, near Ocala) - and the air-boat experience is a lot of fun - and quite interesting if you like wildlife up-close.
Gatorland had a big fire recently - not sure if they are fully operational again yet. Personally, I find the place a bit offensive (not that I'm a lentil munching tree-hugger or anything), it's grubby, exploitative of the animals and a bit hi'billy, if the truth be told.
Saturday night cruise in Old Town, Kissimmee is OK to see once. The 800 cars claim is a bit of a stretch, but there's a fair old collection of rods, muscle-cars and historics - I say OK to see once because the same folks show-up week in, week out.
Depending on how fat in't wallet you are, you might like the Warbird flight experience in Kissimmee. You get to 'front-seat' a T6-Texan - but I think it's in region of $300 a throw (up).
As MGMark states, Daytona Beach has a real automotive history (The LSR attempts were actually run at Smyrna Beach) - but there is not a lot to see/do on the sands at that time of year. Depending on the beach erosion situation, you may not even be able to drive on the beach, as per normal. There is some good related stuff at the Daytona USA exhibit at the Speedway though - worth a visit, without doubt.
Take Randy up on his offer - the gulf coast is great and there are some great attractions on that side of the state. The Florida Aquarium in Tampa is really good and Ybor City (northern historic district) is like Bourbon St, New Orleans at the weekend. Check-out/Google The Sea Screamer at Clearwater - and there's lots to see and do at St. Pete.
You are not going to be short of things to do, Andy.