We've been twice and tried two things. We always arrive late morning (having left on an evil morning flight) and are at the resort by noon. Swimming is a priority no matter what. The first time, we swam, and then went to Epcot. But between lunch, swimming, and checking in, we didn't make it to Epcot until 4pm. It was fine, we did Illuminations, but I decided next time we wouldn't do a park and "take it easy."
When we went last time we also got in early and made it to the resort at lunchtime. We went swimming for a while and ate; went to Downtown Disney for a while, then Chef Mickey's for dinner. Frankly, after an early morning flight (and lack of sleep-- I never sleep the night before a trip)-- this didn't really qualify as taking it easy! We were still running around a lot and the Kid passed out on the bus.
Next time I resolve to REALLY take it easy our first day and just relax at the resort-- swim and veg by the pool, nap, and have a nice dinner at the resort. Some people like to go-go-go on their first day. In theory, I like the idea, but I think if I relax and soak up the resort vibe I'm in better shape for touring. Just my opinion!