I never saw in the packet advice on using taxi's, hotel shuttles, etc from traveling from the raleigh/d airport to chapel hill... maybe someone who has been there can give me some advice?
I think taking a taxi from the airport is going to be expensive. UNC is a good 25 min from RDU. There are buses to and from the airport and to and from Chapel Hill that you could check out. gotriangle.org is the website for the bus line.
Priceline.com has rental cars for $26/day. It would easily be my preferred choice - allows you to see the area a bit more. You only need to pay for parking ($6, I think, at the hospital garage) during the interview. IMO it would be the easiest and most RELIABLE means of transportation. Good luck.