We leave on Sunday too!!! We will be going to a park that day though, but if we weren't, we'd probably swim for a while, get something to eat, check out the resort, hit DTD.
We leave on Monday!!! We won't get in until about 7:30 p.m. so we'll probably just enjoy being at the hotel, however in the past we've gotten down there early and had a whole day before our pkg. starts - on those days we've gone to DTD and also toured some of the other Disney resorts - checked them out to see if we might want to stay at one of those another time, we also will go to the Poly that night and get a drink/food and watch the fireworks from there. Having a full day is nice because it gives you a chance to slow down and enjoy your hotel or check out others, something when you're in the parks, you usually don't take the time to do. So excited just thinking about it! I'm in Disney World in 5 days!!!!
We have annual passes so we do have tickets for our first day; we plan on heading to the Magic Kingdom. If we didn't have tickets we'd go to Downtown Disney to shop, browse, and/or eat,and spend some time relaxing at the resort.