I was in Raleigh for a few weeks in 2002. Unfortunately I only had one weekend off work and I decided to do some sightseeing by car instead of flying. A colleague was there for a year or so and did about half a FAA PPL from RDU. I will try and get some local info from him tomorrow. I seem to remember he visited various local airfields for training, but all flights originated from a club at RDU.
You should plan a trip to Kitty Hawk which is not too far from Raleigh. There is a small museum and memorial to the Wright Brothers and the field where they took to the air for the first time appears not to have changed much in 100 years. There is a small airport close by.
TG.
I forgot to mention the weather.
I was there in summer and it was steamy hot. I have never known humidity like it and there were thunder storms late afternoon most days. Late morning / early afternoon was clear blue skies but too hot to linger outside. I think Autumn is supposed to be pleasant with temperatures in the high 60s / low 70s. Much better for flying.
Raleigh itself is surrounded by trees - millions of them. This might make local flying a bit boring? At RDU you will be mixing in with all sorts of commercial traffic, which could be fun, or scary, or probably both!