Charlottesville is definitely not rural, and I definitely would not refer to UVA as a rural school. Charlottesville/Albemarle County is surrounded by some rural counties, but that is true of many places outside of NOVA (including Richmond).
I'm surprised that you did not know that, living in Williamsburg and all! 🙂
Also, if you are judging what the town is about based solely on its geography, you would probably be pretty far off. Charlottesville is very different from the rest of central VA, I would say. It is fairly liberal for the area, has a lot of culture and history, etc. It is very beautiful, which you may know just from geography -- lots of trees, nice mountains. Sorry if you knew all this already!