Agreeing with others here -- if you can rent a car, just for a day, do it. We weighed other options and decided it would be worth it to have our own vehicle. We reserved an economy from Alamo and it was under $45 for a day. I figure with that and gas for 300 miles, we'll still be under $100.
We're planning to do the space center in the morning, spend a few minutes on the beach, then catch dinner in Cocoa Beach and stop at Super Target on the way back to the hotel. No way we could afford to do that with a shuttle or taxi.