Assuming you live in Oklahoma City, it's about an 8 hour drive to Albuquerque (longer from Tulsa).I need some feedback from the experts on the below: is this insane?
If you wanted to maximize your time in NM and AZ, by doing a long drive at the beginning and end of your trip, you're looking at a 5 day loop starting/ending in Albuquerque (or possibly Santa Fe, or better yet starting at one and ending at the other).
A hectic five day loop (Starting Albuquerque/ending Santa Fe) might look something like this (assumes about 5 hours driving max per day):
Day 1: Drive to Albuquerque
Day 2: Albuquerque -> Acoma pueblo, Petrified Forest -> Flagstaff (5 hour road time plus sightseeing... long day)
Day 3: Flagstaff -> Walnut Canyon, Sunset Crater, Wupatki: stay in GC at Yavapai Lodge or the like (two hour drive but lots of sightseeing)
Day 4: Morning at GC, 4 hour drive to Monument Valley (or Kayenta)
Day 5: Morning tour at MV, 6 hour drive to Taos
Day 6: Morning in Taos, 2 hour drive to Santa Fe, afternoon in Santa Fe
Day 7: Drive back home
THIS IS NOT A RECOMMENDATION!
I'm trying to help you visualize what a loop might look like; you need to decide how many days you have, and how to break up your time. There are other loops you could do (I would recommend trying to go out one way and come back another), and the choice of what you want to spend time seeing on a particular loop is the next set of choices you have to make.
I picked these because they are either iconic, or fun, or just because I like them. I believe this trip is doable. Lots of scenery for taking pictures of, some Native American options (Acoma, Monument Valley... make sure you get some fry bread and Navajo Tacos somewhere along the way), and spots where there are a ton of easy walks.
I would suggest your next move is to decide how much time you have, and target your loop... then we can help you further with specific options.
Final note (and this may be controversial): for a female traveling alone, trying to maximize what you're seeing, I would recommend pre-booking your reservations. You probably don't want to find yourself at the end of a long day looking for a place to sleep.