Nobody's mentioned "Captain Wedderburn's Courtship" (Child #46?) -
The Laird o' Roslin's dochter. Roslin's just to the south and Wedderburn House is just to the East of Edinburgh.

Apart from that there's "Sandy Bell's Blues", "Old Bell's Barroom", "The Dying Folksinger" (as I walked down to Sandy Bell's barroom) & "Edinburgh Bus strike Blues". And my mother used to sing a song with the chorus "Edinburgh once more"