I miss Santa Fe's extensive hiking trail system.
One of my favorite hikes (Atalaya Mountain Trail) showcases the valley where Santa Fe sprawls. While I love the hike, I don't love the crowds. I go early to avoid them. Or I branch off to Dale Ball Trails on a left fork about 1/3 of the way up. There is a small wooden sign marked for those hiking down so it is easy to miss. This branch is much less traveled, very scenic particularly during spring run-off, and is very well marked.
The La Cieneguilla Petroglyph Trail is a poorly maintained (I personally love this) 2.4 mile round trip hike to a huge number of ancient rock drawings. I saw a couple of people when I was there, but it mostly seems out of the way with only a little signage. If you have bad knees, think twice; I did some minor scrambling. If you are the type who worries about getting off-trail or lost, you might want to take someone with you who doesn't. The trail is often ambiguous, but I never felt confused because the land is open and you can easily find your way back to your vehicle.
Bandelier National Monument cannot be fully appreciated in one trip. I've stayed at their campsite, and it was wonderful except for the doofuses who arrived at the next campsite at sunset and spent the next 4 hours bumbling around in the dark trying to set up their tent and generally being loudly annoying.
A couple of day trips to this park, which is nearly an hour from Santa Fe, are not enough. I saw cliff dwellings, looked down on ancient kivas, and climbed long ladders up to lookout points. A side trip to a petroglyph area (look for a small sign that says "Petroglyphs" a couple of miles before the entrance to Bandelier) was amazing. I saw hundreds of pottery shards and almost no people.
My favorite hike is the Upper Rio en Medio. Here's why: