Dog friendly beautiful landscapes to visit in southern Utah?

The only thing you're doing in Colorado is the Four Corners Monument? That would be a very bottom of our list.

Each national park has an awesome web site which will give information on pets in the park and other helpful things.

Grand Canyon NP does allow pets on the Rim Trail.

Zion has a very nice paved trail for dog walking and biking.

Here is Bryce's take on pets:

https://www.nps.gov/brca/planyourvisit/pets.htm

Look up the other parks you'll be going.