Installed on the wall of the Great North Museum, you can see it on the lane that cuts through from Claremont Road to Devonshire Terrace, more or less underneath Claremont Bridge. It represents St Mary Magdalene.
The sculpture comes from the St Mary Magdalene Hospital, the original 12th centurty hospital was more or less on the spot now occupied by St Thomas Church and assisted and treated lepers.
The 12th century hospital was replaced in 1874 when a new facility was erected behind the Hancock Museum
In 1874, the hospital was moved to a new location behind the Hancock Museum. That building was demolished in the 1960's. Of course it wasn't a hospital in the sense we use the term these days, the 19th century building was more of an alms house, akin to the Holy Jesus Hospital. In 1959 38 bungalows were erected at Spital Tongues to contunue the tradition of providing accommodation for the elderly.
Of course it is debatable as to whether the sculpture is from the 12th or 19th century building, if I was a betting man I would tend to go for the latter.
This is an image of the 19th century hospital, courtesy of the Newcastle City Libraries Flickr Photostream: