There's a simple way and very scenic. If you're staying in Grand Canyon South Rim then exit via Hwy 64 east to Hwy 89 at Cameron. Take Hwy 89 north to Page, AZ and continue on 89 West to Kanab, Utah. This would be a good stop to tour Best Friends Animal Sanctuary if you're an animal lover. It's a no kill facility in awesome surroundings and you won't find anything similar.
From Kanab, Ut. take 89 south a little way into Arizona at Fredonia, AZ. Then take 389 west which becomes 59 in Utah to Hwy 9 in Utah at Hurricane. (This part of Hwy 9 is just about flat.) Then either find a park on east Hwy 9 all the way to Springdale or stay in the park at Watchman campground. If staying in Springdale the park's free shuttle stops at various places in this small town.
You didn't say where you're heading after Zion but I'd recommend Bryce Nat'l Park. To get there backtrack on Hwy 9 west to I-15 and head north to Hwy 20. Take that east to Hwy 89 and go a little south to Hwy 12 taking you to Bryce. Stay in the park or just outside the park entrance at Ruby's RV. Hwy 12 from 89 to Bryce is again, just about flat. Hwy 12 from Bryce to Torrey? You probably won't like it although many, including us, do.
๐ However, if you want to get to Torrey to tour Capitol Reef Nat'l Park there's an easy way - from 12 take 22 north to 62 to 24 east to Torrey. Lovely drive.
When leaving Zion you don't want to take Hwy 9 east to 89. That's a big climb with switchback leading you through the tunnels. You won't like it!
All of the above are very doable with an RV with no major climbs or switchbacks. It's the easiest route. Have a great trip! By the time you do these parks you'll be a pro.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel