I assume you are attending grad school at NC State. There are several older (post war) apartment buildings nearby that are filled with students and recent grads. They are in excellent locations.
Check out Raleigh Apartments
Raleigh Apartments. They are walkable to NC State, Cameron Village and the entertainment districts downtown.
There is also a collection of apartments directly across the street from St. Mary's College on Hillsborough St. These too are very convenient to NC State.
All these apartments are less expensive than new ones. They don't have amenities and they are older. But, they just might fill your needs within your price range. But, I will say that I'd set my expectations closer to $600 than $500 a month.