Satisfy the culture vulture within at Saint Nicholas Museum. See if there are any guided tours or ask a museum employee to direct you to some of the collection highlights.
You'll have no end of sightseeing choices when staying in Demre. Saint Nicholas Museum is a great place to start here, but there are loads of other fine spots to explore. Myra Ruins, St. Nicholas Church, and Andriake Port Ruins are near the museum and will top off your day nicely.