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Bringing a wailing baby to hushed Blue Hill would be a faux pas. But for well-behaved tweens, executive chef and co-owner Dan Barber’s West Village haunt is a great introduction to the good epicurean life. Here, the evening may begin with a seasonal spin on a pig-liver terrine or vegetable soup, and move on to a sweet, slow-roasted parsnip “steak” with creamed spinach and beet ketchup ($32). If the kids don’t have a taste for, say, Block Island tilefish ($34), a mound of sides made with goods from local farms, including the nonprofit Stone Barns Center for Food & Agriculture in Westchester, should do the trick.