Hello and welcome to the RTA forums !

The advantage of driving a loop is that you will avoid one way drop fees on your rental. As for what you should do with your time really comes down to what interests you and grabs your attention. Why New Mexico for example ? Are there things along route 66 that really interest you ? At the end of the day it's just a bit of 'black top' and much of it was decommissioned many years ago and replaced by Interstate.

What I recommend you do is dig around the forums and trip planning pages here at RTA and gather info through research, look at maps and see what appeals to you. Once they are marked you can see how to join the dots and we can help with that but we can't make meaningful suggestions until you have a least the basics clear in your mind. What I will say is that between LA and Denver you will be near to a number of great National parks, scenic drives, mountain towns etc throughout the Four corners region and you could make an amazing loop trip with 3 weeks at your disposal. If you wish to go to Yellowstone that could also work. Enjoy the planning !