Luquillo is just a 15-moment generate to Fajardo, which has other truly wonderful beaches. You can also get to Ceiba in less than 30 minutes and take the ferry to Culebra or Vieques.
Some wonderful beaches to visit https://tiannanlwx643521.wikidirective.com/6782367/little_known_facts_about_beachfront_vacation_rental_puerto_rico