I'm looking for some recommendations for backpacking routes in New Mexico in late May. I'm planning to fly into Albuquerque on May 17th and then have several days of flexibility in my schedule. I'd like to find some backpacking and hiking for about four days, either stringing together one long 4-day/3-night hike or some combination of shorter trips with some day hikes. I'm willing to drive a bit, so I've seen options including Pecos Wilderness, Guadalupe Mountains NP, Petrified Forest NP, Gila Wilderness, Lincoln National Forest, Bandelier National Monument, and more.
I originally looked at the Pecos Wilderness as I will eventually be visiting family in Santa Fe and it has great mountainous terrain and vistas, but it looks like it's likely that there will be significant snowpack still at that point, unless I keep to the really low elevations.
I also looked at the Gila Wilderness, specifically the West Fork or Middle Fork trail to Jordan Hot Springs, but it looks like trails aren't very well marked in a lot of places and I don't want to worry a great deal about orienteering or constant navigation.
Also, my partner is joining me, but we will only have one car, so loops are greatly preferred, unless there's something like a shuttle available.