Palazzo Reale just off Piazza Pleblescito in Naples is a beautiful reminder of past royalty from the steps at the entrance that the Neopolitan King used to walk up while riding his horse to the family crests lining the walls in one of the ballrooms. The tapestries are beautiful, yet worn- as is much of the palace. There are magnificent paintings, and inlaid wood pieces. The palace is definitely worth visiting and much of it can be seen in a few hours. Just outside is the Teatro San Carlo, Piazza Pleblescito and great shopping in Via Roma.
Seeing the inside of the palace with all its art and architecture was nice (I love the intricately carved wooden door designes), but I would say the outside is worth a visit too (& free).