Take an overnight trip to a scenic alpine lake in the Pecos Wilderness, just outside of Santa Fe, New Mexico. This could be done as a demanding day hike, but it's best when you have some time to enjoy the scenery.
Accessible June through October, snow lingers on the trail late into the summer. This is a very popular, well-marked route so if it's solitude you're seeking, you'll probably be disappointed. At least on the weekend.
The trailhead is at the parking lot for Ski Santa Fe. You'll climb from 10,250 to 11,700 feet elevation at Lake Katherine. If you're feeling ambitious, you can hike Santa Fe Baldy from the saddle.
There are several different routes you could take, so pick up a detailed map and scope it out for yourself. We did this as a lollypop loop hike, spending one night at Spirit Lake (which we had to ourselves) and one night at Katherine (which we shared with a large number of folks, but surprisingly it didn't feel too crowded).
Do note that camping is prohibited within 200 feet of the lake, and is monitored by volunteer forest rangers. They will require you to move your camp if it is too close.