Although it’s possible to get to your hotel and some of the islands’ beaches using publicos (shared vans that carry multiple fares at a time), to fully explore the islands’ remote beaches a rental car is recommended. Book early though, because they go fast.
Vieques  and Culebra  are such small islands that it’s possible to spend a day and a night on each one to get a cursory feel for them both. But the reason most people go is to experience the islands’ unparalleled natural beauty and soak up plenty of R&R. To do those things properly, it takes a few days to reset your internal clock to “island time” and achieve a blissful state of total relaxation.