The first one to avoid in an RV that pops into my mind is UT-261, the Moki-dugway. It runs from UT-95 near Natural Bridges National Monument to Mexican Hat. Part is paved, but the really steep part is gravel/dirt. There are a number of youtube videos of it.
Another that comes to mind is AZ-89A through Oak Creek Canyon and then the section from Clarksdale to Jerome and Prescot. I believe there is a 40' length limit. I have driven this many times in the 23' long bed crewcab and that is about as big as I would want to go. Getting through Jerome is tough with tight turns and cars parked on the streets.
BIA-13 between Chinle, AZ and Shiprock, NM has steep grades and swichbacks and I believe a length limit. I drove it in a 27' Class C. Lots of second gear both up and down.
The road through Salt River Canyon, which is between Globe and Show Low, AZ is US-60/AZ-77. It is a major truck route through that area, but does have steep grades and switchbacks.
US-191 from Threeway, AZ to Alpine, AZ has some steep climbs and a low clearance tunnel. I drove this section in the 27' Class C. It took forever. It is a renown motorcycle tour road. Further North, US-191 has steep grades and ten switchbacks in nine miles North of Vernal, UT. It then goes up and down through Flaming Gorge.
I second the recomendation to get a copy or download of the Mountain directory.