Carol
Puerto Alcudia really has two centres - the Bellevue area to which Tootsie refers, and the port itself. The Bellevue area is more lively. In the port there is the Alcudiamar Botel, right in the marina. 4-star. See
http://www.almarsa.es.
Like the Paraiso, this offers apartments in a hotel environment. If you want apartments only, with a sea view (which really means direct by the beach), the options are a bit limited.
Feel free to PM me if you want more guidance.