We did the exact same route your planning just this past summer. We had no problems at all...road from I-70 into Hanksville was excellent and from there into Torrey was more scenic and twisty, but still very good road conditions (we were towing the Jeep). I'll second (or third) Thousand Lakes RV...we only stayed there 2 days (we are not hikers)but enjoyed our stay.
If you have the time or plan on going into Bryce Canyon and Zion NPs, I also would recommend taking 12 SE. We had planned on staying between Bryce and Zion(Long Vally Junction), but didn't like the campground, so we went a little further into Glendale on 89. Anyway, the first 1/3rd of 12 is an uphill challenge towing the Jeep, but we took our time (sometimes @ 20 mph)and the views were waaay worth the effort. Hell's Backbone is worth every white knuckle. It was a little intimidating but no problem towing or negotiating the curves...just spectacular scenery! When coming down off of the Backbone, it's a 12-14 % grade...I just put it in 1st gear. Didn't have to hit the brakes much cause you really can't go much faster anyway and didn't feel like we held anyone up. !2 is possibly my next favorite road of the whole trip. Road to the Sun, in Glacier came in first.(that one is definitely a toad road!)
After skirting Bryce, hang a left(south)on 89. There are a few CGs on 89 but we really liked Bauer's Ranch in Glendale. Nice park and even has a donkey welcoming committee. We stayed there a week and backtracked into Bryce to have a better look and also explored Zion. Of the 17 National Parks we visited, Zion was at the top of our favorites list. Then if need be, I-70 is just west of Zion. There were a few road construction sites in most NPs this past summer, but most delays were short. Safe travels, Bob
Edit: Heck, if ya got the time, keep heading south on 89...the North Rim really isn't that far away...We couldn't stay in the park so we stayed at Jacob Lake @ Kaibab RV Village and drove the Jeep in. : )