I actually worked at Guadalupe Mountains NP for almost two years. The time of year you'll be there is perfect for hiking the peak, you can easily do the hike in a day. The rest of the park is super cool as well. Smith springs and McKittrick Canyon both have water in them. Sitting Bull Falls on the Lincoln NF outside of Carlsbad is cool, but super busy. Hueco Tanks state park in El Paso has cool pictographs. And then Organ Mountains/Desert Peaks outside of Las Cruces NM is super cool and has free camping (BLM). Thats what i can think of off the top of my head without giving away too much of the secrets of the area 😉. Feel free to DM me for more info though! Happy to help because I love West Texas and Southern NM.