What is the best route from Phoenix to rapid city?
Depends on what you mean by "best route". The shortest route from Phoenix goes through Flagstaff to Grand Junction and Casper to Rapid City The route I think Hazel is recommending is longer but more interesting to goes to Albuquerque Trinidad (Colorado)Colorado Springs Denver and Cheyenne
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Take I-10E to 25N to 90E. Drive 6 hours a day. Stop at all caves and museums and markers. Buy post cards.