We always fly in the night before and stay at the Hyatt, then take the
DCL buses to the port the next day. The Hyatt is more expensive than the off-airport hotels, but I think this is offset by the convenience of having the hotel right in the airport terminal. This way, you don't have to find a shuttle to get to your hotel, its just upstairs from the baggage claim (at least the one Delta uses). Check-in for the DCL buses is in the Hyatt lobby, and you can leave your bags outside your room in the morning and the bell service will collect them and hand them over to DCL, who will transport them to the ship. The Orlando airport has a fair-sized mall, and there are plenty of choices to eat, from fast food, to a sit-down dinner. As far as what to do that night, we usually arrive in the evening, check in, take a shower, then grab some dinner. By then, it's late enough that we'll just watch a movie in the room and then go to sleep.
The busses leave the next morning at around 10:00, getting you to the port by 11:00 or so. I think the transfers go for $49/person round trip. Again, this way (Hyatt/DCL bus) costs a bit more, but is very convenient and saves you a bit of standing around and waiting in rental car lines, for hotel shuttles, etc.
I suppose if you arrive early enough, it might be worth renting a car and heading over to the WDW resort for the evening. You could also use the rental to drive to the port the next day. Several companies have offices near the port and allow you to rent one-way without a drop-off charge. Most have shuttle service to the port, or will reimburse you for a cab. Among those are
Avis, Budget, and Hertz, and there may be others. If you choose this option, you can purchase one-way transfers to get back to the airport after the cruise. I think these go for $25/person.