Our kids have slept over on Tom Sawyer's Island (they even have rocking chairs at Aunt Polly's, but I feel guilty taking one for so long, so I usually just find a shaded spot and sit on the ground). It's really hard to get a stroller over there, but if you have an umbrella type that reclines, it's not impossible.
Next to space mountain, where the old ski lift station is, there is a nice quiet spot back in the back. The train goes buy there, but it doesn't blow it's horn. (at Aunt Polly's, the riverboat blows it's horn) The only problem with the area is that, because it's so secluded, we've had rude families use it as a smoking area a couple of times (saw my kids, along with the kids of several other families, sleeping....didn't care. Loud, coarse language, smoking, kids climbing trees).
In Epcot, I would recommend some of the back gardens in the countries. Canada has a beautiful garden as does Japan.
We've never stayed through a nap at MGM or AK. We actually usually go back to the hotel for a nap...mommy likes to nap too!