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There are tow main options for your drive, neither of which is significantly longer and both of which certainly offer their fair share of scenic and historic attractions. The 'northern' route would use I-15 up into Utah and then follow I-70/I-76/I-80 to Chicago and would hit Las Vegas, Zion, Bryce Canyon and Arches National Parks, cross a gorgeous section of the Rockies and then follow the old Oregon Trail along the Platte River. The 'southern' route would turn off I-15 earlier and follow L-40/I-44/55. This is essentially the alignment of the storied Route 66 and brings you near the Grand Canyon, Albuquerque and Santa Fe, Cadillac Ranch, the Ozarks and St. Louis.
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AZBuck