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Betatakin Ruins is located inside of Navajo National Monument on the Navajo Nation, and is available to visit as a guided tour from the Rangers at the monument. The hike to the ruins descends into the canyon for a very strenuous 3 mile round trip hike, with about 700 feet of descent into the canyon.
When Janet and I visited Betatakin a couple of years ago, we mentioned to our guide that we had recently climbed the 300 steps down to the lighthouse at Point Reyes, and he laughed and said something to the effect of "we have a few more than that here." According to the NPS website, the switchback trail to Betatakin has 927 steps.
Link to google maps: Betatakin Ruins