Bandelier's 1.2-mile Main Loop Trail in Frijoles Canyon offers an excellent introduction to the main ruins and history of the park. The trail first passes Big Kiva and the Tyuonyi ruins, the original 14th-century pueblo on the canyon floor. From here you'll climb alongside the cliff face, where later caves were carved out of the soft volcanic rock (back-room additions to structures built outward from the cliff). Short ladders enable you to clamber into the alcoves. The self-guiding booklet ($2) is recommended.
A further half-mile up the canyon is the Alcove House (or Ceremonial Cave), the highlight of the park for many, in particular children. Located 140ft off the ground, it's only accessible via four wooden ladders and while it's not dangerous, it is a bit thrilling – although for some, it may be too head-spinning.
In addition to a number of other shorter hikes, some 70 miles of trails traverse a rugged backcountry with further ruins to explore. Unfortunately, severe environmental damage – a wildfire in 2011 and a torrential flood in 2013 – has made backpacking trips to destinations like the Painted Cave more of a challenge, though not impossible. Be sure to check in with rangers about the feasibility of overnight hikes.
Note that you cannot drive to the main visitor center and Frijoles Canyon between mid-May and mid-October. Access is by a free shuttle that departs the White Rock Visitor Center in White Rock.