Luquillo is simply a 15-moment drive to Fajardo, which has other truly beautiful beaches. You may as well get to Ceiba in below half-hour and go ahead and take ferry to Culebra or Vieques.
I advise renting a car or https://medium.com/@villaazurepr/top-vacation-rentals-in-puerto-rico-a-guide-b35afd204830