We don't do any "non-park" days, but we do have "down days" -- they're simply a much more relaxed day than our full park days. I will mention that we usually visit Disney in late June which means long park hours and hot afternoons. Our typical routine is:
Day 1 (arrive at Disney World resort around noon). Have lunch & unpack. Spend a few hours in a park (usually Epcot). Get to bed at a decent time.
Day 2: Rope drop at MK. Afternoon break (3-4 hours) return to MK in the evening. Stay until we're tired (usually 9-10:00)
Day 3: Rope drop at EP. Depending on what we got accomplished on day 1, we either just push through and stay at Epcot until late afternoon and then return to the resort for the rest of the day OR we take an afternoon break and return to Epcot in the evening OR if there is an EMH night at MK, we might go there.
Day 4: Sleep in. No plans until after lunch. Morning spent swimming, hanging out at resort, etc. Go to DHS or AK for a few hours. Possibly hop to Epcot or MK depending on what we feel like doing. Or we might return to the resort for some swimming.
Day 5: Rope drop at DHS. Afternoon break. Return to DHS that evening.
Day 6: Rope drop at AK. Either stay straight through the day until dinner and then return to the resort OR take afternoon break and return to AK in the evening.
Day 7: Sleep in. Head to DTD for late breakfast/early lunch. Shop. Return to resort to pack and possibly swim. Hit a park in the evening -- usually MK but could be one of the other parks depending on what we feel like doing.
Day 8: Leave for home early in the morning.
We try not to do more than 2 "long" days in a row. And if we know we're going to have a very late night (like MK EMH), we always follow it with a sleep-in day. We used to do a "no park" day in the middle of our stay, but we felt like we were wasting our vacation time just sitting at the resort watching TV and doing a little swimming. When we realized that it was only going to cost us $10/person (at that time) to add another day to our tickets, we changed our ways. Unless we're going to be at Disney more than 9 days, we will always have park tickets for every day of our stay even if we only spend a few hours in a park some of those days.