Check out boxcanyonblog.blogspot.com
They have a park they stay in at Zion every year.
"November in Virgin, Utah, at the Zion River RV Resort. Ahhhh. We'll once again take advantage of their $430 dollar per month winter special, along with their pool, hot tub, endless hot water showers, and convenient location."
Bryce is too far away to enjoy from the same spot you'd stay for Zion. Red Canyon near Bryce has a nice campground.