I will be going to mesa verde next month and wonder whether any place to stay is better than others

The most convenient is the Far View Lodge right on the property. Call right away, as it may already be filled up. Otherwise, you're probably best off staying in Durango, which, if my memory serves me correctly, is 13 miles away.

From the entrance of Mesa Verde to Durango is more like 40 miles. Cortez would be much closer. You would be best to stay in the park if reservations are available because it is quite a drive just from the entrance of Mesa Verde to any of the dwellings.

Oops, I guess my memory is failing me. I guess it was Cortez I was thinking about, i.e., 13 miles away.

One of the nicest places I've ever stayed was at the Blue Lake Ranch, halfway between Mesa Verde and Durango.
It's a Bed & Breakfast on a 100-acre property, with a main house and several cottages. The grounds are full of flowers and absolutely gorgeous, the rooms are lovely, and the breakfast is
wonderful, with friendly guests standing
around nibbling and chatting while the owners cook. We paid about $150 a night (about 5 years ago) and thought it was well worth it. The phone number I have is (970)385-4537.

Have fun!