Bandelier National Monument
Official links to:
Location: 30 minutes from Los Alamos, NM
Maps: Custom Online Google Map With All stop
GPS: Google Earth KMZ Garmin GPX or GDB Other
Operations: Year round. Winter check official website.
Fees: $12 for entry for 7 days. (OR Park Pass)
Nearby: Chaco Canyon
Must See:

This is NOT officially in the Red Loop.

Only if you are have chosen Albuquerque as your starting point should you see this to your itinerary, unless you want to of course (it would add 8 hours more of driving time).  But you will get plenty of Cliff Dwellings in Mesa Verde National Park which is in the Red Loop.

If you love Cliff Dwellings, but actually climbing into them, this is one of the best self guided parks. It’s a very small park and you can see most of it in a few hours with some light easy hiking. (Main Loop Trail is 1.2 miles round trip)