Zion - we stay at Watchman C.G. in the park. That's the electric one. The non-electric one is too small for our 40' MH. Leaving Zion to the east you'll have to pass through the tunnels and there are some size restrictions but you didn't say what you'll be driving. Google the "Zion Tunnel" for the official National Park website information.
If you don't want to do the tunnels or can't because of size, you can easily take a couple other routes. The scenic one is west to Hurricane, UT and picking up UT59 to AZ389 which will take you into Fredonia and Hwy 89 north to Bryce. You could also pick up the North Rim of the Grand Canyon a little way off this route from Jacob Lake. Oct. is beautiful there with the aspen trees in full color. We stay a DeMotte Nat'l Forest campground just outside the park's entrance but the park has a campground, also. Check the website for closing dates.
Another way to Bryce from Zion is back onto I-15 to HWY 20 east to 89 South. Don't take 14 unless you like steep drives.
Bryce - we've stayed in the park's campground although there is Ruby's RV just outside the entrance. We really like Red Canyon forest service c.g. west of Bryce but, again, you'd have to check closing dates. Last Fall we found both Zion and Bryce comparitively empty in October and it was a pleasure to tour them once again. We've been to both often.
From Bryce to Monument Valley - a few choices: Continue from Bryce on Hwy 12. We find it very doable in our 40' but you'll hear comments about how scary it is. It all depends on your confidence level. It's a good 2-lane but it's a mountain road with beautiful scenery taking you through Escalante. Then from 12 pick up 24 to 95 into Blanding, UT and Hwy 191 south to 163 to Monument Valley. Nice drive. Don't plan on taking Hwy 261 from 95 to 163 at Mexican Hat. It's an extremely steep, curvy, narrow partly gravel downhill.
Or from Bryce get back on 89 north to 62/24/95/191/163
Or..from Bryce get back on 89 north to I-70 east to 191 south. This way you can take in Arches and Canyonlands Nat'l Parks and Dead Horse Point State Park (great campground with magnificient views) and then continue south to Monument Valley.
Monument Valley - Gouldings RV is the only park nearby. Monument had a dry camping spot right in front of the famous 'Mittens' but I think it's closed right now for renovations. You'd need to check it out. That's where we stay.
Lots of road choices....have a great trip!
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