I live in Puerto Rico and been to Luquillo many times. It is a beautiful beach! I don't know if the ship offers a shore excursion or if you'll have time to do it on your own, it is about 1 1/2 from the pier. It is a public beach and the entrance fee is $1.00 or $2 per car
I'm not too sure. One thing to keep in mind. Depending on the day you are planning, if you decide to drive, be aware that rush hours in Puerto Rico are murder! If I can help you in any way let me know.