Look at Kanab, Utah as a base camp for the Zion area.
Kanab WebsiteI've been there in April. It was a bit windy and the town really doesn't get their season started until May but it has a good location.
Moab is its own stop. Arches is having construction this year on their roads, be aware of that. Canyonlands is there. Dead Horse Point State Park is there.
Capital Reef NP is nice too if you want to spend a day there on the way from Moab to Zion. You can stay in the park in Fruita (no reservations and not very big campground) or just outside the park in Torrey. Escalante is a town a lot of Utahans go to but I don't know if out-of-staters go there.