Ruby's inn at Bryce Canyon is a great place to stay, just outside the park. It is at 7,600' elevation. I think the highest point on the drive is around 9,200' elevation. THere is one lookout that has a arch just a few feet from the roadway.
Ruby's Inn has a hot tub, full hookups, and all that. Temperatures are nice in August.
Are you also going to Zion NP? It is only about 85 miles away. Don't worry about the tunnels, they are fine- I took a 40' Country Coach through them, towing a Jeep.
The North Rim of the Grand Canyon will be open in July, also at 7,500' elevation, it will be nice, and has lots of boondocking places to stay in. Ask the rangers for a good place.
Fred.