It's all about the people you know and the friendly controllers. Try giving the Raleigh-Durham ATCT a call at 919/840-5544. That's probably not the direct number, but if you need one, call a local FBO or nearest FSDO and ask for one, they'll likely have one.
Most of the up and down class c facilities (TRACON and Tower in same building/location) are really nice about getting time in both environments (TRACON and ATCT); RDU is an up/down facility in case you didn't know that.
Usually the towers/tracons are pretty accomidating when they have enough staffing (eg: HPN won't let me come up on Saturdays because there are no supervisors, but any other day works), but it's up to the tower chief or air traffic manager.
Some are more strict than others, but it shouldn't be all that difficult. If you need further help, PM/e-mail me and I can see if one of my controller buddies knows someone at RDU.
Good luck,
Jason
P.S. A ride is a great treat anyway! The tour is just icing on top of the cake.