Caffe Driade is a hidden gem in Chapel Hill. Located on Franklin Street, but far away from the hustle and bustle of campus, it can be hard to find (the sign is small, and not too well lit at night) but it's worth it to turn around if you drive past the first time.
I had the best latte in my life here, and the atmosphere is very cool. It's quiet enough to read a book or study, as many of the patrons were doing, or to have an actual conversation with your date. When I went, it was too cold to take our drinks outside, but there is outdoor seating, which some brave souls were taking advantage of.
Highly recommended, especially when they are having an art show (very frequent).