loggia n 1: a roofed arcade or gallery with open sides stretching along the front or side of a building; often at an upper level
Loggia \Log"gia\, n. [It. See {Lodge}.] (Arch.) A roofed open gallery. It differs from a {veranda} in being more architectural, and in forming more decidedly a part of the main edifice to which it is attached; from a {porch}, in being intended not for entrance but for an out-of-door sitting-room. [1913 Webster]