I agree that it really does depend on your kid. We just stroller nap, because my son WILL NOT nap in the hotel room. We've tried bringing him back and it just resulted in major tears and tantrums and major frustration on my part.
If I just push him around he will fall asleep and stay asleep for at least two hours. He'll do this in any kind of weather, I guess he is just used to it, seeing as how we live in DC and walk everywhere, all summer long. I do have a stroller fan to help keep him cool.
We usually do rider swap for the adult rides (the adult with the kid waits in an air conditioned shop), or just take in the scenery and details. We take lots of pictures, we enjoy shopping in World Showcase, we sit down with a drink, there is plenty you can do at WDW without riding rides.
My favorite parks for pushing around a napping little one are Epcot and Animal Kingdom. In Epcot you really can experience most of WS (except the rides and movies) and we just walk around, get snacks and drinks and actually get to enjoy adult conversation.
In Animal Kingdom, we often hang out in the dawa bar, or we enjoy the animal trails.
DHS is a little more of a challenge, but you can get drinks to go from the Tune In Lounge, and just hang out on the streets of America.
In the MK, we've ridden lots of rides via rider swap, we've driven the RC boats near Jungle Cruise, gone to the Frontierland Shooting gallery, and played Skeeball in the arcade at the exit of Space Mountain. One time we sat outside of one of the shops in Frontierland and played checkers. We've even taken the monorail over to the MK resorts for a drink.
I actually love stroller nap time, because it gives DH and I time to connect just to each other. If I wasn't pushing around a giant stroller, it would be almost like we were on our honeymoon again!
So, really there are plenty of things to do in the parks during nap time!
