What are you looking for as 'sweet'? I find the Monument Valley to be a real treat as well as some of the red rock / rim rock of UT. The problem is weather. If you aren't well equipped for cold weather, you are vulnerable to either freezing or being stuck somewhere. I'm about 400 miles east of you. We had 60 degree days and 45 degree nights up to Sunday when the nights went below 20 and today it'll be only about 48, but it'll warm.
I make that point to say that this time of year, you can have cold fronts dramatically change the weather once you are north of your current location.
I suppose you could take the far south route to Big Bend, tour around that interesting place in TX and then return being fairly safe from weather which would overwhelm your riding outfit. I find the southern deserts to be beautiful and interesting, but that may be because being a native, this his home to me. Others only see sand, cacti and scorpions.
Your other route would be to Yuma then San Diego for a run in SoCal which is always interesting and would tend to be clothing appropriate as it's never bitterly cold there.
Why be born again when you can just grow up?