That's the Castel dell'Ovo in the background. Fun fact, it's named the Castle of the Egg because supposedly Virgil (yes that Virgil) put a magical egg in the foundation, and if the egg was ever broken it would destroy the castle and bring great misfortune to Naples. The castle standing today was built in the 12th century A.D, but the original nucleus was started by Greeks in the 6th century B.C.
People often look at me weirdly when I tell them I rather visit a museum than go to the beach (not to shame anyone, I mean, to each their own). But let's be honest here; would you rather stare at the same blue puddle each day or have the chance to see an almost perfectly preserved mosaic in what used to be a bath house about 2000 years ago? I was fortunate enough to visit this place on my travels and it is moments like this that I am reassured in how I like my vacations: hot, dusty and with a certain challenge which mostly leads to me being more tired upon my return than before I left.