Photography
Most of the major Chaco pueblos are photogenic, but a few tips to improve your chances of getting some good shots:
These ancestral pueblos are known as great houses, and they are massive. Wide-angle lenses are useful.
Many of the "commercial" shots that you see are difficult for the average traveler to duplicate, because you're required to stay on the trails and the requirement is enforced, limiting your opportunities to get shots from above. Views of the Pueblo Bonito and Chetro Ketl sites are reached by trails that do lead to vantage points above the ancestral pueblos, and are therefore better suited for this kind of shot than some others.
Fajada Butte
As in many such sites, photographs taken during the middle of the day can look somewhat flat, particularly in the height of summer. Plan on using your camera at sunrise and sunset if feasible. Fajada Butte, one of the park's iconic features, is particularly attractive at such times, with shadows that create interest.
You'll have a hard time incorporating much green and growing vegetation into your shots, but the vegetation, such as it is, is most photogenic early in the spring if there's been some snow and again early in the fall.
hike
There are four trails leading to remote pueblos, all available for day use and closed after sundown. Probably the most interesting is the trail to Peñasco Blanco pueblo, which has become famous for a well-preserved pictograph thought by some to represent the great supernova of 1054. This pictograph is under a rock alcove below the main Peñasco Blanco structures. Please treat it respectfully; this is a rare find in the world of anthropology. Note that this trail crosses a wash that can be dangerously full of water if there have been thunderstorms upstream.
All trails require free permits available at the visitor center or the trailheads. Hiking boots are a good idea, and carry plenty of water. Off-trail hiking is generally not allowed.
bike
Bicycling is a good way to get around the main tourist loop, and in addition, there are two backcountry trails that offer mountain biking. Wijiji trail is shared with hikers and is a short about 3 miles, easy ride that should take under an hour. A more serious undertaking is the ride to Kin Klizhin, an "outlier" site archaeologically related to the main canyon sites but well removed from the canyon itself. The ride to Kin Klizhin takes one southwest out of the canyon and into some very lonely country, and is about a 25-mile round trip. Go well prepared with water, repair kit, etc.
stargaze
The exceptionally dark night skies of Chaco provide good opportunities for amateur astronomers who bring their own telescopes, but even better, in 1998 the park opened its own observatory (http://www.astronomy.org/...) with a large 25" telescope and modern equipment that the visitor can share. During the summer there are interpretive programs by park staff, supplemented by members of The Albuquerque Astronomical Society (http://www.taas.org) who bring equipment, give lectures, etc. Information on the program may be available at the Society's web page, but the Chaco information does not appear to have updated since 2004.