The west of America has some of the most awe-inspiring scenery I've ever seen. If time is very limited, fly into Vegas and drive down to the Grand Canyon, north rim, via Bryce Canyon or Zion National Park. Not only will you get a taste of life on the road here, I guarantee you'll be blown away by the landscape. You can find motels or lodges on National Park land for little money ($50 (£25) a night will get you a decent place) and all the crappy diner food you could ever want.
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