Little Hawk, I would be wrong to claim that McGonigal was a great poet but I must correct your assumption that Leith and The Water of Leith are the same thing.
Leith (as of the Leith poleith) is the dockland town to the north of Edinburgh.
The Water of Leith is a stream that meanders through Edinburgh to meet the North Sea at Leith.
Dean Village is an area of greater Edinburgh half a mile or so northwest of the west end of Princes Street (the castle is on Princes St). modern map here
Telfer's bridge over the Water of Leith at Dean Village is where McGonigal's poem is set. Old map and pics of Dean Bridge and St. Bernard's Well