The flying goat is located at the top of the hill, which was a nice walk in the evening form where we were staying. we ate outside overlooking the golf course. our server julia was so nice, knowledgeable about the menu, and friendly throughout our visit!. View the menu for the flying goat and restaurants in shelter island heights, ny. see restaurant menus, reviews, hours, photos, maps and directions.. Flyinggoatrestaurant.com is tracked by us since september, 2018. it was hosted by linode.. flyinggoatrestaurant has the lowest google pagerank and bad results in terms of yandex topical citation index..