You get off the ship pretty early (well, we were the slow pokes getting off, but some folks get off earlier) so you'll have the whole day after your cruise to kill. We flew home that afternoon (early afternoon), but if you're not flying out till the next day, I'd suggest finding something to do!
You can rent a car in Port Canaveral and go to Disney, Downtown Disney, Universal, just hang out, but if it were me, I'd stay somewhere more fun.
If your flight is super early the next morning, I'd still look at renting a car to go somewhere fun for the day before going to the Hyatt. There is only so much you can do there for basically all day.
PS: Must do? We stayed at the Four Points by Sheraton Cocoa Beach the night before our cruise. Rented a car from Budget (I think) and DH ran to the store to get a bottle of Grey Goose (Disney allows liquor to be brought onboard), some wine, and I forget what else. Our friends bought a case of water (and the stewards just slapped a tag on it when they dropped it off with their luggage so it was delivered to their room). So if you want to pick anything up for the cruise, a rental car is nice to have!