Alcudia is a versatile port; there's not one obvious main attraction. A low-key wander around Alcudia makes for a perfectly beautiful day, especially if you want to purchase gifts that aren't touristy-tacky or sample some local Mallorcan or Spanish cuisine, such as pa amb oli: bread with olive oil and tomato, topped with cheese or local ham.
Sun-worshippers can escape to beaches like Platja d'Alcudia, while history buffs will enjoy a stroll through the Roman ruins of Pollentia. (Take a tour for more information, but the site has good signage and is walking distance from Alcudia so a tour isn't mandatory.) Other tours include trips to Palma, local wine tasting and 4x4 rides through the countryside.