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]