So what universities is he applying to?
One major piece of information missing, is whether you are doing this all in one, trip, or several.
Most of the cities you mentioned are a fair drive from each other, just too short to make it worthwhile to fly, too long to really want to drive. BNA-ATL is about 5 hours, ATL-RDU is 6-6.5. MIA is kind of a long way from anything.
One tip I can give concerns car rentals. Most one-way rentals these days do not have a drop charge per se, but they come with a significantly higher daily rate. Sometimes you can use points for one-way car rentals, often you can't. It's worth investigating, because a "Free day" is worth a long more when it's a one-way.
However, another major point, if you rent a car, is to consider renting off-airport. Depending on the location, airport surcharges can be huge, and are often a percentage of the rental. I was considering a road trip starting in DFW and lasting a week, and I found that if I rented the car at the airport it was $900, but if I rented from a Hertz location about 3 miles away, it was $500. So a $20 cab ride would save me quite a bit.
Obviously, use Priceline for your hotels. In case you need it,
http://www.flyertalk.com/forum/onlin...ng-primer.html.
I live in RDU; PM me if you have any specific questions about the area.