One of the best would be to land at Aspen, take a bus into town, then shuttle to the Maroon-Bells trailhead. From there, you can do a 3-4 day 4-pass loop, which is spectacular:
Land at Montrose, CO, rent a car, then drive south to San Juan mountains. There are 10+ backpacking trips that are world-class. Let me know if you need more specific recs for that area, as I spent years exploring it.
From KLAM, you can actually backpack from the airport. Go through town, and get to the Pipeline trailhead (35.89544352665885, -106.33311631398587). From there, you access 100+ miles of trails around the rim and valley of the Valles Caldera National Monument.