When I was at Yellowstone Park, there were no chargers in the park that I could find. However in Grand Canyon, they were way more than generous and let me charge for free in Trailer Village!
Hey! Look what the Manager of the Zion NP Lodge sent me! It doesn't want to load - I'll try to add it later - a nice pic of her LEAF charging there. I think public car travel is allowed up the canyon road (where the lodge is) during the off season, October - March (??) otherwise, it's the shuttle. the visitors center is on hwy 9 tho, which is accessible year round. Also pipe springs is a whole separate place far south, but hey, that's another charger. The more the merrier.