Located just outside of the Mallorcan capital, the imposing Castell de Bellver is one of the rare circular castles in Europe. Built as a residence for King James II of Mallorca in the 14th century, the castle saw its primary use as a prison for centuries before being used as a tourist attraction in recent years. Inside is the city's history museum and the uniquely circular courtyard, among other attractions that are telling of the castle's place as both of a royal and defensive structure. Climb to the top of one of the towers to get a lovely, panoramic view of Palma del Mallorca and the adjoining coast.
If you're sick of the beach and feeling a hole where your cultural initiative used to be, fill it with Castell de Bellver.