If you're a fan of live theater performances, book yourself a seat for a play at Radu Stanca National Theater. Look online for times and prices.
You'll have sightseeing choices galore when in Sibiu Center. Radu Stanca National Theater is a great place to start here, but there are many other worthy places to explore. Piata Mare, Liar's Bridge, and Dumbrava Sibiului Natural Park are not far from the arts and culture attraction and will top off your day nicely.