You can definitely do it.
Be real about it. You are on vacation. Sleep in a bit. Go have breakfast at one of the resorts. You can always do freshly ground coffee at the Poly with a danish, too. Visit a resort or two and just take it all in. Take in the theming. You can always go to the pool and just relax. Sit under an umbrella and read a book. Have lunch by your resort pool. Take a nap in the afternoon or watch an hour of TV just to get out of the sun. Make an appointment at the Grand Floridian Spa and then go to high tea. Relax at the Poly while waiting for the fireworks to start.
You can always hit DTD as everyone has mentioned. If you are adventurous, try the mini racing boats or the paddle boat. You can always rent a bike at numerous locations throughout the resort. At night, there is a free bonfire and if you like smores, you can purchase a kit to make them.
I would treat this vacation like any other beach vacation. You are there to relax. Spend time playing miniature golf. Other suggestions were good too: fishing, boating, horseback riding, etc. If you're really daring, go for the race experience at the race track.
Don't forget resorts do offer tours of the individual resorts. Wildnerness Lodge has a good one. You can have a quick lunch at the quick service place while you're there.
