The flying goat restaurant is located in the shelter island country club, a historic, wood-shingled structure with a wrap-around porch. the porch is the place to sit and it overlooks the golf course with distant views, in each direction, of the water.. 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..