NC Central would probably be willing to give you money- though they're dirt cheap as it is if you're an in-state resident. Are you a resident of NC?
The last question really is necessary to figure your chances at UNC. You're in good shape with your GPA (though not great), and at least in the middle 50% for the LSAT, but it would take a very strong application otherwise and residency (I think) to get in there.
Otherwise, Tulane might be a good fit for you- though I don't know if that's east coast enough for you. They seem to have a very good (surprisingly even) reputation in the southeast. You're really looking regionally, though, so I think you need to consider places you'd like to live in particular...and then go from there.