If there is a public square that needs to be experienced while in Naples, it is the Piazza del Plebiscito. Flanked by two wonders of neo-Classical design, the San Francesco di Paola and the Royal Palace, this large, open square is full of pedestrian traffic and has long been a cultural meeting place for Neopolitans. There are two stately equestrian statues in the center of the square, which is within a few minutes of other attractive, salient points in the city (Nearby is Piazza Trieste e Trento and its lovely fountain, as well as as the popular shopping promenade Via Toledo).
Be warned, though, the area suffers from the use of graffiti and the refuse of people passing through. Despite this, Piazza del Plebescito still throbs with the pulse of history and is still a popular gathering place for both locals and tourists. There are a handful of cafes nearby if you're looking to linger for a while with an expresso or a snack.