Probably the best side trip you could take while visiting WDW. It's a little longer about 70 miles from inside WDW. Once you get away from the World traffic is pretty free flowing and once past the airport no problem. You do take a toll road so keep that in mind.
You can get on the 528 from WDW a few ways but once you get on that going eastbound you take 407 north, the Freeway kind of splits 528 continues southeast. 407 splits off and goes north, it's just a two lane highway called the challenger mermorial parkway. It makes a T with 405 in a small town. Take a right on 405, You exit this small town and go by a building with a space shuttle. That's a separate museum, the main visitor center is across the waterway. I'm not sure what the current cost is, I went back a while and it was about $50 for an adult or child, I'd guess now it's about $65-70.