Definitely the Sansevero Chapel Museum, the National Archeological Museum, the San Carlo Opera House, Underground Naples and the Santa Chiara church/cloisters.

Definitely the Sansevero Chapel Museum, the National Archeological Museum, the San Carlo Opera House, Underground Naples and the Santa Chiara church/cloisters. The downtown subway stations have unique designs and art of all sorts, too. Or artifacts discovered during the digging, in one case later incorporated into the design of the station itself. Finally, you can easily spend half a day just trying out pastries.