The NC Museum of Art has a nice permanent collection and often brings in really cool exhibitions. The permanent collection is always free. The sculpture garden is lovely in the spring and summer months. The museum has concerts and movies outside in the summertime as well. The temporary exhibitions are usually excellent and well worth the price of entry. They're now open til 9 on Friday nights, making the museum a great date spot. I really enjoy being able to stop in, wander a bit of the permanent collection in a spare half hour of my day, then come back later. If you're not as local, the guided tours and such can allow you to make a full day of it.
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