Our DD is 6, so it's been over a year since she napped at WDW. She used to do it all the time, though - only an hour or so as she got older, but she didn't usually have a huge problem falling asleep in the stroller anytime.
In the MK, we often sat at either El Pirate y El Perrico or the Tomorrowland Terrace while my DD slept in the stroller. We'd walk her around until she fell asleep, then we'd get a cold drink and settle down in a quiet, coolish (or at least shady) area for her to nap. Tomorrowland Terrace is air conditioned, so it was nice when it was hot.
At AK we'd do something similar, but there are lots of little out-of-the-wayish areas that you can park a stroller and sit while a small one naps. You can find tables at the restaurants (Flame Tree, Pizzafari) best at non-mealtimes, though - they get packed around lunch!
At Epcot, we liked the Electric Umbrella (somehow, we were always in Future World) but I think the restaurant in America would be nice and cool and relaxing as well.
At DHS, I honestly don't recall what we've done. I think we've sat near the Backlot at the restaurant area there once or twice.
The great thing about just resting while the little one naps is you get a much-needed break as well. It give you an opportunity to go over plans for the rest of the day, get a snack or a drink, use the restrooms, people watch and just get off your feet for a little while!
Amanda