There's a boat that takes bookings from the huts by the bus shelter / marina that offers fishing trips. Interesting though, that even their poster doesn't show anyone with anything particularly big. From the beaches / jetties you'll find the usual Med. species - Mullet, Gilthead Bream (Dorada) and various little stripey bream type fish. License wise, officially you do require one - however, I'm told that it's a real pain to get one, involving a trip to Inca, passport copies etc. I've been visiting the port for 20 years and fished on every occasion and never been asked for one. I get the impression that the police are far more interested in locals fishing for the pot, rather than holidaymakers fishing for a bit of fun.
(Hope that hasn't tempted fate!)