You didn't say what you like to do and when you'll be doing it but I'll throw in my opinions. I've hiked in over 30 US National Parks and lived in the South West desert and these are my highlights. The south west can be blazing hot (brilliant advice, I know) so it would be best in May or early June.
1) The Grand Canyon is my favorite place in the world. If you don't mind driving a long dirt road (60 miles? I forget) you can camp about 50 yards from where this picture was taken at Toroweap:
If you're by yourself you might feel isolated and you need to be prepared because you're a long way from a tow truck.
2) Zion NP is amazing and has my favorite hike in the world,
Angels Landing (Google image search). The most popular hike is The Narrows, a slot canyon with the Virgin river flowing through it:
More Narrows pictures (Google again)The only problem with Zion is that it can be tough to get away from crowds if you go after school gets out.
Not too far away from Zion and GC are
Bryce NP and
Lake Powell, both worthy sites. Together these parks make up the so-called Golden Circle. You can stay in Kanab, Utah, at
Parry Lodge where old-time Western movie stars used to stay while filming in the nearby canyons.
3) I found Yellowstone to be amazing if you're willing to do a short amount of walking/hiking. 95% of the visitors don't go more than 500' from the roads and boardwalks so you can find some beauty all your own. Yellowstone is maybe our most unique park with geysers, hot pools, and huge waterfalls. If you're into botany you can see how the park has evolved from the huge fires they had 20 years ago. Yellowstone might have the best wild life viewing of any NP.
Just south of Yellowstone is the Grand Tetons (insert juvenile boy snickering here) with perhaps the single most picturesque view in the US:
4) Yosemite isn't my favorite park, probably because I had been to the GC and Zion previously so I wasn't awed as much as others who see it first. Plus it's super crowded in the summer and it's hard to get away from them However, it's one of the most popular parks for very good reason.
If you're making it a long road-trip (which would make me very jealous) I'd also suggest these parks:
- Devil's Tower (Wyoming)
- Humboldt State Forest (Cali redwoods)
- Crater Lake (Oregon)
-
Canyon de Chelly (N. Mex)- White Sands (N. Mex)
- Monument Valley (Utah/Ariz)
- Mt. Rainier (Wash)
- Sequoia NP (Cali)
Sheesh, I'll stop now; if nothing else you've allowed me to reminisce so at least I found this post interesting.
The most disappointing park I've been to was Joshua Tree NP in California. I fell asleep in the car.