Our residency state is S. Dakota though we "get outta Dodge" and spend winters down South (AZ, TX, or FL). We spend alot of time in the beautiful Black Hills and have often traveled to AZ from the Rapid City area. Just for your comparison, we run a 45 ft. MH towing a Honda Element.
Anyway, the suggestion to take Rt. 79 South out of the Rapid City area connecting Westerly to the North & South running Hwy 18/85 in Wyoming down to Lusk, WY then Westerly again out of Lusk on Rt. 18/20 over to I-25 South to Cheyenne and on South through Denver, Colo. Springs, etc., is likely your best route.
Pick a favorable weather window and after leaving Rapid, figure staying overnight in Cheyenne. In fact, consider an overnight at the Terry Buffalo Ranch RV Park immediately on the South side of Cheyenne. Aint fancy, but very nice, easy in and out, AND, have supper at their restaurant on sight. Wife says to try the Honey Glazed Yard Bird (Chicken)..mmmm,...mmmmm,...GOOD!! There's also a easy in and out fuel stop at the exit just a mile or so before
the campground exit (forget the exit #) but you'll be topped off ready to enjoy a relaxing evening and an easy get-away the next a.m..
Now, we travel at around 62 to 64 mph and very comfortably make it through Denver (take bypass around WEST side...it's easy!!) on through Colorado Springs, and on down to Raton Pass on I-25 all the way by the 2nd evening. (Re: Denver bypass...coming South on I-25
, take exit #216
(Westerly) onto I-76
. In a few miles take exit #269
easily flowing onto I-70
(still heading Westerly). At exit #460
on I-70 take bypass #470
Southward around West side of Denver and looping back to your original I-25
route at South side of Denver and you're on your way.) This is a no problem bypass. You'll like it.
Anyway, if ya DO get to Raton Pass the 2nd evening, consider an overnight at a cute little campground atop the pass. Now...we had NO problem exiting at the top of the pass at the Colorado/New Mexico weigh station and looping over the I-25 freeway over to this little campground. It's a little jig-joggy but sure was a nice stop. You're a little later in the year so check weather and call the campground first. If weather is no good, stay in Colorado or go over the pass before holding up for the night.
Then, stay on I-25 down through Santa Fe to Albuquerque where you'll pick up I-40 West to Williams, AZ. Would strongly recommend a night or two in Santa Fe and try the Blue Corn Mexican Restaurant in downtown which is the heart of Santa Fe. A great one or two night campground is called Santa Fe Skies just off I-25 as you get to the SW side of Santa Fe. Can't recall exit but it'll be in the book or on-line.
We'd also recommend an overnight at the Meteor Crater RV Campground as you head Westard from Albuquerque into Arizona on your way to Williams. Great, simple, clean little stop right at the SW corner of exit #233 (I think) into the Meteor Crater visitor center.
Have a great trip.
Steve & Lynette