The hilltop monastery of Puig de Maria, on a 333-metre crag two kilometres south of town, has views that take in the whole Bay of Pollença, the Tramuntana, and on a clear day the island of Menorca far to the east. It was founded in 1348 by Augustinian nuns and has been almost continuously inhabited since.
You can drive most of the way up a steep, narrow paved road, then walk the last 20 minutes; or do the full hour-and-a-half walk from town. There is a simple restaurant at the top, and the old cells have been turned into a hostel where you can spend the night. The atmosphere is genuinely monastic — bring a torch if you stay over, the lighting is minimal.