For Zion, check if Watchman CG within the park will be open. They have electricity but no water, so you'll need to take it on before heading in. There are also numerous private RV parks within Springdale but we stayed at Watchman and loved it. For Bryce - check out
Ramblin Ralph's Website- he just recently stayed near Bryce and south of both Zion and Bryce in Kanab. He has information on both on his site along with GPS coordinates and pictures. He's got lots of great information up here. When we've gone to the Grand Canyon, we've visited the North Rim most often, but that is high elevation and closes earlier than the South Rim, but is by far the prettiest and best, in my opinion. In Jacob Lake, north of the entrance, there's a FS CG at the junction. There's also a FS CG on the road to the North Rim and numerous boon docking sites on the road behind this CG. I believe that Ralph has boon docked there and lists it on his site for one of his travel years. You may be able to fit within the park, if it's open still. With snow already in parts of Montana and the East, it may be coming soon down there too. Oh, and near Bryce there's also Ruby's Inn and a CG within the park, but I don't recall how big the sites are. We stayed at Ruby's Inn and liked it.
2011 Bighorn 3055RL, 2011 F350 DRW 6.7L 4x4 Diesel Lariat and Hensley TrailerSaver BD3, 1992 Jeep ZJ and 1978 Coleman Concord Pop-Up for remote camping
Dave & Renee plus (Champ, Molly, Paris, Missy, and Maggie in spirit), Mica, Mabel, and Melton