There are more interesting parts of the city than UNCC (Uptown/Downtown, South End, Southpark), but if you're set on staying there, take Blue line uptown and get off at Convention Center station.

Note that it will be NYE, and as it gets later, they'll be lots going on downtown beyond the football game. Also Charlotte's downtown is pretty compact, so you can walk around to pretty much anything. You can even walk to South End (Breweries, etc.).