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Two weeks is a fair amount of time for the trip, but it's really too short a time to justify buying a car. That task, difficult enough for someone here, becomes extremely difficult for a foreign national with no local address. Besides, the cost of taxes, title, licenses, and insurance add up quickly and the time spent searching for a car and trying to sell it at the end would eat into your trip time. On the other hand renting a car one-way will not be cheap either. You should be prepared to pay in the neighborhood of $200/week for the rental, $300 for the one-way drop-off charge, and $350/driver surcharge if you and/or your mate are under 25 years old.
Your basic route across the southern tier of states would be I-10, but you would have some time to wander off the main road if you so desired. Highlights would be Las Vegas and the Grand Canyon if you want to head up that way; the deserts and Indian cultures of the Southwest; San Antonio, Austin and New Orleans; the bayous of the lower Mississippi and the Gulf Coast; and of course all the attractions of Florida including Disney World or the Kennedy Space Center.
AZBuck