Probably a long, thin, wooden gallery running east from close by the Banqueting House. Replaced by brick in 1669. (Information from the Latham & Matthews Companion volume, p.478.)
The overlays that highlight 17th century London features are approximate and derived from Wenceslaus Hollar’s maps:
Open location in Google Maps: 51.504856, -0.125581
"A wooden gallery, location uncertain, but probably that from the Banqueting House, passing at right angles to it between the Great Court and the Pebble Court, eastwards to the block which included the Great Hall and the Chapel. If so, it was replaced in brick in 1669." (L&M Companion) http://snipurl.com/nw26i
A diagram of Whitehall Palace. The gallery described runs vertically down from the entrance to the Banqueting House.adjoining the Palace Gate. http://www.londonancestor.com/maps/whitehall-pala…
Chart showing the number of references in each month of the diary’s entries.