Drive from Montana to Arizona

I would have them avoid Arches--there's not much to see without some hiking. It is pretty, but you can only see Delicate Arch off in the distance without a 5 mile hike. BUT it is beautiful and there are LOTS of cool rock formations, with a short 1 mile loop walk (sometimes less). I would steer them towards Zion National Park, and Bryce National Park (both also in Southern Utah). Zion's offers guided bus tours, and doesn't allow much (if any) private care traffic. It has kept the scenery picturesque, and you don't have to find a parking spot. 

If they end up in Salt Lake they should come see the temple grounds in downtown Salt Lake (I know, but they have some beautiful landscaping and historic buildings).  On the way out of town, at the south end of the Salt Lake Valley there's a place called Thanksgiving Point that has some gorgeous gardens. I hear that's not to be missed (I keep saying I'll walk through someday...). 

There's always the Olympic Park up in Park City, as well as shopping and the quaint feel of the older part of town, with walkable shops and restaurants. 

And most of the local ski resorts are beautiful this time of year, and offer rides on their trams and ski lifts to get e birds-eye view of the mountain surroundings. 

I second the vote(s) for Sedona-it's beautiful down there! 

If I can think of anything else, I'll holler. It really just depends on the types of things/settings they like. 

When are they going?

Beartooth Highway (Montana, NE of Yellowstone) is a great drive. 

Other than that, plan at least a little ahead.  You may find that the next place for gas is 2+ hours.  The town where you were going to stay is booked and the next town that might have a hotel is another 3 hours. 

No, some towns have *two* gas stations at the same intersection!  

Coming back from CdA, things got a little testy after 11PM and we still didn't have a hotel.  It isn't like we drove past a few and said "nah...we don't need to stop here..."  Between 8PM and 11PM, we didn't drive past ANY hotels, and when we finally got to some, they were full.