If you will be in Colorado, then I will throw a vote in for Mesa Verde NP, near Cortez, CO. It would be roughly midway between Royal Gorge and Grand Canyon, NP. If travel time is a concern, the routing will be something you have to look at closely in CO and AZ; quite a bit of travel on two-lane US or State highways.
02SE is correct about National Park popularity. Most big parks have been setting new attendance records every year. I was at Arches NP, UT, briefly last Wednesday because I was travelling northbound on US 191.
Amazed at the amount of people and traffic in the park. Not overflowing like in the summer, but some parking lots out at the attractions were nearly full.