I have a few thoughts. This may be a fun evening to go to the Magic Kingdom to just keep it simple and wander through some stores, maybe ride an attraction or two, and settle into a good position to watch the parade and fireworks with little snack, like ice cream, since you are having a late lunch.
Oftentimes, too, we like to just spend our first day at the resort by enjoying its offerings and a long dip in the pool. We then get to bed early so we can be fully rested to be at at park when it opens the next morning.
We've also used our first day arrival to visit other resorts. If you are visiting during the holidays, resorts like the Wilderness Lodge, Animal Kingdom Lodge, and especially the Grand Floridian are worthy of a visit.
You may also find going to the Boardwalk a fun adventure. Perhaps you'd enjoy renting a surrey bicycle to work off some stored up energy after traveling all day.