Moving from NYC will probably be a big change, but there is definitely still a lot of fun stuff to do in the Triangle (Raleigh, Durham, Chapel Hill). Southern Village Apartments are nice, a little pricier than other apartments in the area. I think there are a good amount of professionals/grad students in them. Southern Village is on several bus lines also. Meadowmont Apartments are similar to southern village (from what I have heard). I live in Chapel View Apartments, which are nice because the price includes utilities (elec., water, cable, internet), you can get a furnished apt. if you need it, and the bus runs very frequently. They have one and two bedroom apartments and are geared towards students. However, they are pretty quiet and I think there are not too many undergrads in the complex. Website: http://viewstudenthousing.com/. Mill Creek is close to campus, but it is mostly undergrads. Any apartment complex off of Martin Luther King Blvd. would have access to the NS and the T buses, which run quite often. If you look up chapel hill transit, you can find all the info. about the bus routes and compare that to places you are looking at.
A lot of grad students actually live in Carrboro, which can be closer or just as close to campus as Southern Village. There are also several bus lines that run in Carrboro and if you bike it is a great location for that. I don't know too much about the apartments there, I would just avoid Kingswood, Abbey Court, Pinegate, Estes Park, and any other properties owned by GSC Apartment Communities. They are really cheap...but you get what you pay for. I looked into Hillmont apartments, which are one bedroom places in Carrboro, but I never actually viewed them so I can only say they look nice from the pictures I've seen. Craigslist for Raleigh/Durham/Chapel Hill is a pretty good source for privately leased places, especially places close to campus. If you want roommates, there is a section for that and they normally say whether they are grad students, etc. Sorry for the rambling post! Just let me know if you have any other questions