This gracious monastery stands atop the 548m hill of Puig de Randa. Like most monasteries, it was built partly for defensive purposes, though the views are simply divine. Ramon Llull lived here as a hermit in the 13th century, praying in a cave (open 10am to 2pm, ask for a key from the cafe reception), and in the 16th century the Estudi General (university) in Palma created the Collegi de Gramàtica here. You can stay the night (doubles €53–65, suites €80).
The views across the plains to the Serra de Tramuntana are quite extraordinary. There's also a museum and an attractive and well-tended garden and you can eat or simply have a coffee at the monastery's cafe, with outside seating. Driving up here is no problem and there's ample parking. The Santuari, which is variously signposted as ‘Santuari de Cura’ or simply ‘Cura’, is 5km beyond the small village of Randa, southwest of Algaida.