There is only one flight school at RDU. There has been some changes of management and alot of rebuilding work in the GA area since my friend was training there, but it seems that Flight Gest, .
www.flightgest.com/fg/ are what the school has become. They were very good, apparently, and the rates posted on the web look reasonable.
There was an FAA office on the airport.
No circuit training is allowed at RDU due to the busy commercial traffic, so your checkout(s) will involve flying from RDU to one of the local grass strips for circuits.
One other thing, which may not be obvious if you are not a regular US visitor, but you will NEED a car! RDU is about 45 mins from downtown Raleigh, and getting around Raleigh itself is very difficult by public transport.
Have fun,
TallGuy.