Since I live here I'll offer some options
The Kennedy Space is great! We went all the time growing up...especially if you will be here during the last 2 shuttle launches!
St. Augustine is beautiful and a lot of fun. Tons of stuff to see and explore like the Fort and the Old Schoolhouse, they also have ghost tours, etc. Must eats here include the Columbian Restaurant and Osteens (my favorite!!!!!)
If you like to shop the Millenia Mall is like heaven! (but really its great shopping and they have a Cheesecake Factory and PF Changs). There are also two different really good outlet malls (one is at the east end of I-4 and the other closer to Disney).
If you are a race fan the Daytona International Speedway offers tours.
Seaworld and Universal are both fun! And Aquatica is a great waterpark!
And of course the beach!
As a native we tend to avoid I-drive (except to eat a Maggiano's) because it is always crowded (especially during the summer!)