Daytona is worth hitting, but the folks there tend to tattoos and motorcycles and what Americans call White Trash, rather than the posh university set.
But its a small place. If there is a motor race when you are there, see it, but realize that the town will have 100,000+ people in town. The Daytona 500 is at the end of Feb, Bike Week (motorcycle festival) is the first half of march, there is a country music fest over memorial day weekend and a major race on July 4. If you go when there is an event going on it will be quite an experience but finding a place to stay will be difficult
Spring Break will be going on in roughly mid-March which sound good but Daytona as a spring break destination is probably second tier, and will attract far more men than women.
The SEC schools are great for tailgating, but football season is long over and wont' begin again til September. Tickets are not hard to come by since the stadiums are huge, often bigger than professional sports stadiums. Face value of a ticket might be $50-$100. Usually you can buy a ticket for close to face value if you have any skill negotiating, and probably 95% of games you can buy for no more than double. Yes, the games are wildly popular because there are only a dozen a year, and half of those the team travels to the opponent's site. An average game is proabably equivalent to a derby. Most schools will have one or two long-standing rivalries, and the tickets for those will be more difficult to come by. Occassionally a game has championship implications, and there again the tickets will be more difficult.
Based on your itinerary, between Charlotte and Atlanta are Clemson, SC and Athens Georgia, home of the University of Georgia, both of which are probably a better stop than any of the schools in North Carolina. Both are solid universities for gaming, probably 30,000 students, although Clemson as a town is very small. You'll come to that one first so check it out and stay a night or two if you like it.
I think you are going to have a great trip, and will experience a wide variety of the U.S. Miami and the southern half of Florida is much different from the South, and Texas and especially Austin are very different. If you have any flexibility, I would move your trip to September or October because the weather will be more conducive and you'll be able to catch some of these football games. Most of the schools you want to visit are in the SEC conference, with a few in the ACC. You can find the schedules here:
http://www.espn.com/college-football/schedule/_/group/8 You'll see ads for tickets now from a place called stubhub - that is a legit way to buy tickets but don't be discouraged by the prices now will be much higher than you'll actually pay outside the stadium. As to the weather, where you are going it will be mild, so you won't have any problem, but for the people who live there it is relatively cold so for example they won't be having outdoor parties like they will in the fall.