Locavore Restaurant between NYC and Beacon
If you plan on having lunch when you first arrive in Beacon, I highly recommend Poppy's Burgers and Fries, on Main Street in Beacon. It's a very casual place with amazing burgers. The beef comes from Kiernan Farms, which is a local farm in Ulster County. Their other ingredients are mainly grown locally as well. They also have a veggie burger and a couple of other types of beef related sandwiches (sloppy joe, short rib).
I highly, highly recommend the Tavern at Highlands Country Club in Garrison. Much of their produce and meat comes from local sources, including grass-fed beef. I have enjoyed lunch there enormously on three separate occasions. I have not been for dinner, so I can't comment on that, but I imagine it's just as good. It's not far at all from Beacon.
Must trys: lentil soup with pork confit, wings, burger (though I'm not crazy abou the brioche bun), steak sandwich, hot cider, hot chocolate, poundcake parfait with brittle, awesome local beer selection