Mesa Verde National Park does not offer extensive hiking; it is mostly about the views and tours of the ancient cliff dwellings. We did a few short hikes and one of the scenic drives, stopping at overlooks to ogle the artifacts. We did not tour any sites as we are irritable and impatient when in groups.
We hiked Knife Edge, the original entrance road into the park (2mi), Point Lookout for a big view of the surrounding hills and valley (2.2mi), and Soda Canyon Overlook (1.2mi) for a view of the Balcony House ruins.
Mesa Verde was very different from the Utah National Parks both in scenery (green hills and yellow cliffs vs red everything) and solitude (Mesa Verde feels isolated and unpopulated; the Utah National Parks (with the exception of Canyonlands?) are very popular). We should have toured some of the ruins for the full experience, but we still appreciated seeing the dwellings from overlooks and hiking around.