Luquillo is simply a fifteen-moment push to Fajardo, which has other truly beautiful beaches. You can even get to Ceiba in less than 30 minutes and go ahead and take ferry to Culebra or Vieques.
The dry year, from https://medium.com/@villaazurepr/exploring-homeaway-vacation-rentals-in-puerto-rico-d36a888d2a9a