We have done every combination....and have enjoyed each one for entirely different reasons. I think, for us, the least stressful was to stay at Hyatt in the airport and use Disney transfers. But I only do this if we are getting in late in the afternoon/evening. Our kids get a kick out of swimming in the pool with airplanes taking off.
Staying a Disneyworld...I love everything about Disney and so always enjoy this....but usually only do this option if we can stay at least two nights prior to sailing or coming back. With our kids, at least, it's trying to squeeze in so much into one day, go to bed late, up early, and it makes the first day heading to the port kind of a crabby day for most of us. Every once in a while though, I just get the itch to do it, and even though I know it's a lot of hauling luggage and dealing with a rental car, lack of sleep, it just feels like I going home when I go to Disney. It's not logical, it's just a feeling you get.
Stay at the port. I recently did this one this last summer for the first time. We had a car service pick us up at the port and stayed at Residence Inn....it was very nice with a fabulous breakfast in the morning. We enjoyed swimming in the pool and it wasn't crowded at all. That was nice because it's a bit harder to get swim time on the ships for us. We walked a few blocks to a nice place for supper, got to bed early and were ready to go in the AM....no fighting with each other, no one was crabby.....I really think this was more fun than I anticipated.
I guess I can be happy with any of the three options.....enjoyed them all.