Welcome to RTA!

US-40 is an excellent choice from RMNP to SLC, and it's probably the fastest way. Just take Trail Ridge Road west to Granby to pick it up. Figure about 8 hours plus stops. You may want to go through Dinosaur National Monument.

On your way to RMNP via Arches, I'd recommend you take UT-128 to get back to I-70. Also, I'd recommend you take US-6 over Loveland Pass instead of using the tunnels on I-70. To get to Estes Park from I-70, take Central City Parkway/CO-119/CO-72/CO-7. This keeps you out of the congested Denver metro and is very scenic.