An easy trail that takes you along the old Pecos Pueblo and church
The park is easy to get to from Santa Fe. It's about 30 miles SE on the I-25 highway that leads you through Pecos.
Once at the park, the 1.25 mile loop trail begins and ends at the visitor center. Don't forget to stop in there. It's surprisingly nice with some terrific history of the area dating back to the Conquistadores as well as the Civil War.
Don't expect a great workout from the Ancestral Sites Trail. It's easily marked and flat most of the way. It's still a beautiful walk, however in spite of being surrounded by mountains and hills, you still get valley views with big skies only the desert can offer.
Along the trail you will also come across ruins and Kivas (one you can enter). The highlight is the mission church they've been able to preserve enough to let your imagination run while you walk through its doors.
Since you are in the desert, I'd recommend visiting near sunrise and/or sunset if you can so you can watch the shadows and light bounce off the ruins and surrounding hills. The various plants also allow for terrific photography with early and late light that you also can only get in the desert.
Word of Warning: in the summer this place is a haven for rattlesnakes. For a less adventurous experience I'd suggest visiting in fall or winter seasons when it's too cold for them to be active.