I lived in Palma de Mallorca for 6 months. An enchanting place - my wife and I dream of moving back to the island someday and making a home in one of the small, old and hauntingly beautiful towns like Alcudia or Soller.
A 20 minute drive from Alcudia (which I visited today!) is Pollença, another beautiful town (not the nearby Port de Pollença, mind). It also doesn't get nearly as many tourists as Alcudia - if you get back to Mallorca, you should definitely have a visit!