Interstate is I15 N to I70 West. Thats the easy way! Take you 2/3 days.
Byway way? Well, Go I15 just past St George Utah. Take the Zion Nat'l Park exit. Go thru Zion on hwy 9 and enjoy the scenery! OR... if you don't want to pay the park fee just to go thru it, Go a bit further north on I15 and take hwy 14 east thru Cedar Breaks. Either route gets you to hwy 89 north and you can take that back and hook up to I70 West. OR, take hwy 62 to 24 west and come out by Green River (110miles of no service on I170 between Green river and salina).
Off I70 in Colorado take U.S. 50 east to U.s. 285 north. Unless you want to go thru Moab, Utah and head east on ut46/co90 and hook up w/145 so. to 62n to us550 n to montrose and then get on us50.
My fingers are tired now, but you get the idea. Avoid the super slab as much as possible and take 3 days to get where you want to go and you will have a ball!
Went the scenic route thru Utah and Colorado and had no regrets. Got wet, got cold, had a ball! Took 3 days.