There's only one real restaurant in Chilmark, but it happens to be one of the best on the island. The Chilmark Tavern does upscale New American cuisine with minimal pretention. Each plate, from pork chops with mustard crema to braised halibut with fiddleheads, feels thoughtfully curated for their reliably compatible flavors, not showy presentation. The results are worth the drive.
As with all of Chilmark, the tavern is BYOB, but it will happily chill any booze you bring with you, and it even has a list of cocktails that can be made using your home-brought libations.