I really love Big Bend deep down in southwest Texas. It's incredibly remote (70 miles from the nearest major town, 235 miles from the nearest major airport) so you have to have some dedication to visit. It's incredibly diverse, in terms of landscape, flora & fauna and climate. It's also the only national park to have an entire mountain range entirely within the boundaries of the park (the Chisos). It's bordered on the south by the Rio Grande, and the park includes a ferry based border crossing to Mexico at the small village of Boquillas.

There are lots of hikes and plentiful places to camp, plus it's an International Dark Sky park, identified as having the darkest sky in the continental US. I also like that it's the one of the least visited parks in the country, so you can go on hikes and literally see no one else on the trail for the entire day. If you want a park where you can get away from it all, this is the place. All that said, you probably don't want to go in the middle of summer when temperatures are often over 100° F. If you're looking for someplace to go in the fall or spring, this is it.