When you think of cliff dwellings, Mesa Verde National Park is probably the most iconic. Located in southwest Colorado, this may be the first National Park that I visited.
Pro Tip: This is a busy park and timed reservations are required for the major sites of Cliff Palace, Long House, and Balcony House. There are a few smaller hikes and sites that don't require reservations. The NPS site says to book at least three hours between tours (i.e., if you book a 9AM tour, book the next no sooner than noon). However, I was able to make it from Wetherill Mesa to Chapin Mesa in time for a tour two hours later.