Smell the sagebrush
What MeefZah said.
I think you should slim down your itinerary. My wife and I did an 11 day road trip from the Bay Area CA to Zion and Bryce this spring. Except for one long day of driving 12 hours, we didn’t drive more than 6 hours a day. After all, we wanted enjoyment and relaxation instead of a marathon run. Although we were fully equipped to sleep in the back of the 4R, we stayed in motels. We’re hikers so we planned on 2 or 3 long hikes in each national park which required 3 days in each location. My philosophy is this: if you’re planning on just driving through a park and taking photos then driving to your next destination, don’t waste your time. Stay home and look at professional photographer’s pictures. They will be much better than anything you will take.
To really get the feeling and appreciate it you need to get immersed into the wildness of it, even if just a little ways on a hiking trail. Zion is impressive but as Meef said, it is crazy busy. Although in October maybe less than peak season. One day we hiked 3 miles up the Virgin River (The Narrows, see pic below) after renting water boots from the Zion Outfitter. Highly recommended. If you’re not afraid of heights hike to Angels Landing. This probably is the most impressive day hike I’ve ever done. Great views, kind of strenuous, exposure, chain hand holds so you don’t fall to your death. It’s great. Google it and read reviews.
Another great hike but less demanding is Observation Point (pic below, Angels Landing is the knife edge ridge in the center of the pic). But don’t hike from the valley floor. Approach it from the east entrance on the road that goes by the Zion Ponderosa Ranch Resort. There’s some dirt roads out there and even some slight 4WD stretches at the end. Plus you could car camp near the trailhead.
To me, Bryce is actually a more impressive park. It’s smaller and you could just drive along the rim stopping at each lookout and take pix. But refer to my philosophy above. At least hike into the canyon. Start at Sunset Point, hike down Navajo Loop trail and return via Queens Garden trail. About 3 miles. If you’re more ambitious do the “figure 8” loop. To the above trails add the Peekaboo Loop. About 6.5 miles total.
On day 2 in Bryce we did the more ambitious Fairyland Loop trail from Fairyland Point, counterclockwise. 8 miles, but not too strenuous. Wow, what scenery. It’s like being on Mars with all the red rock and spires. Truly a lifetime memory.
Note: the figure 8 Loop is popular with day hikers especially in the first mile or two, which is all the further a lot of families attempt. We passed about 200 people that day. The Fairyland Loop is more remote, we only saw 30 people all day.
If you’re in shape and like to hike, get into the scenery. Just be prepared for sun, rain, carry food and water, first aid, etc.
Plan a little and have fun!