We went to PR last year. We stayed for a couple nights in San Juan, visited the rain forest, then flew to Vieques. We were there for about 4 nights.
We LOVED Vieques. The beaches are among the most beautiful I’ve ever seen. It used to be a military base, so the island is still relatively underdeveloped (no chain stores or restaurants, for example). You have to rent a car and drive to the beaches, 10-20 minutes depending on where you stay on the island. But they are worth it. We also had some excellent meals on Vieques. We’re planning to go back.