What I specially liked about this beautiful town, apart from its appearance itself, is the feeling it shows when festivities are around. Decorations are set from wall to wall creating a kind of white ceiling. I searched for some info and found Alcúdia offers many music fests.
The festivities of the town, in June, offer many cultural activities as well as concerts around the streets, and there are more like those in July (Festes de la Mare de Déu de la Victòria) and Sant Jaume fests. If visiting Alcúdia in August, you might find "Concerts a la fresca", concerts and plays in the street and amphitheatre. But the one I would enjoy the most would probably be "Alcúdia Jazz", in September.