I'm chartering in the SVI for the third time next month. My past trip reports are here:
Islandtime.
Of the beaches on Vieques accessible to charter boats, I like Blue Beach (Bahia de la Chiva) best, but it can be rough for overnight. Definitely get to Playa Flamenco on Culebra -- it's "busy" on weekends, but lays back during the week. It's sort of like Grand Anse (Grenada) on a non-cruise-ship day, but prettier, and has the convenience of kiosks selling local food (we like mofongo so much we named our race boat
Mofongo). My favorite beach is Bahia Tortuga on Culebrita; walk to the end, and enjoy the Jacuzzis (but be sure to wear sturdy shoes).