Erroneously named for the famous Aztec ruler, Montezuma Castle (a national monument in northern Arizona) is actually a Sinagua pueblo set securely in a cliff. Begun in the 12th century and abandoned in the 14th century, at its peak it was six stories high and had 45 rooms. The fragile condition of the structure precludes any access to it; the best a visitor can do is to walk along a paved trail that parallels the base of the cliff.
The cliff faces south, with the structure angled slightly to the east. So the best light on the “castle” is in mid-morning. That information doesn’t seem to be published anywhere, so I’m offering it here.