The space center is definitely worth it, especially now that the shuttle is there on display.
That's more "central Florida" to us locals, though.
If you're into any shopping, Orlando's outlet malls are a big attraction to tourists. And if you miss being so close to Sweeden while you're over here, there's an IKEA there as well.
St. Augustine is a nice town to go and walk around - it's historic and has a lighthouse, some old forts, etc. Good restaurants and such. There's also a pirate ship there for some reason... I forget why.
If you're into nature, you may want to check out the Ocala National Forest and do some camping there. I'm sure you can rent camping tents and supplies somewhere and make a few days out of it.
Other than that, I would drive up the coastline and find a vacation rental on the beach for a week - that may be fun. Look at Ormond Beach and Ormond by the Sea if you plan on going that route.
Just rambling off the top of my head, I hope this helps.
I may just ask you the same when I visit England for the first time (hopefully this summer)