Luquillo is only a 15-moment push to Fajardo, that has other seriously beautiful beaches. You can also get to Ceiba in under half-hour and take the ferry to Culebra or Vieques. Uber isn't out there both, so I recommend https://medium.com/@villaazurepr/exploring-homeaway-vacation-rentals-in-puerto-rico-d36a888d2a9a