We actually look forward to a free day during our trip, and we usually take at least one.
I think whatever you do will be relaxing because you're not in the crazy (yet fun!) parks. Don't get me wrong, I love the parks or I wouldn't even be on these boards, but I love my free day. We stay at YC/BC so we like to relax at Stormalong Bay.
Or, sometimes we have what we call "Fort Wilderness Day." Love that place. We have horses so I use it as my "horse fix" - love to visit the barn that houses the draught horses. Also enjoy the little petting zoo. We've also been canoeing and bike riding at Fort Wilderness and in the evening we enjoy the Campfire Singalong and the hay ride.
Another free day activity is resort hopping. Just going around to different resorts and taking everything in - maybe having a meal somewhere different. And, as another poster stated, if you're going when the Christmas decorations are up this is an espeically good idea for free days.
We also enjoy playing minature golf at Fantasia and heading over to one of the outlets in Orlando.
Then, after all this relaxing fun - we're ready to hit the parks wide open the next day.
PamNC