There's a private garden; from Google Maps it looks like it's mostly around to the right of here, behind a wall. It abutts the back gardens of Prince's Buildings and Windsor Terrace, I think, so might even have a way out onto Prince's Lane, or did have at some point in the past, before everything got quite overgrown back there.
GPS Coordinates:
51.45209, -2.62353
Location: Hotwells