North Riding Infirmary developed into the ENT hospital, so may have been the hospital where your Grandmother was. (Newport Road) (been there - Tonsils aged 5 or 6 - lost a lot of blood - never liked Jello (Jelly) or oranges since.
The General (near "old" football ground - yes I know there was an older football ground) Was originally the workhouse. Accident and emergencies.
My Mother's cousin was last Matron there. She went on to be a member of the hospital board for the area and worked for the modernisation of hospitals (South Cleveland) (So blame her)
West Lane - origanally an isolation Hospital (Cholera, smallpox, typhoid and scarlet fever) Part of Linthorpe Cemetery contains the failed cases, I believe.
(Also floating Hospital on the river)
Hemlington - originally an army hospital. Then isolation (Out in the country at the time - been there too - appendix with complications, aged 10 for 3 months)
Eston - originally Miners Hospital, then infectious cases, then a General.
Others as Barbara says. Carter Bequest - Private patients & union members?
Poole - TB isolation. (Worked on a Farm owned by the head saw bones as a lad. (Dr Walton) TB? - lets crack open the chest and collapse a lung)
Parkside Maternity (next to Nazareth house)
See: -
http://rememberwhen.gazettelive.co.uk/2008/10/index.html?page=2but sadly : -
http://rememberwhen.gazettelive.co.uk/2008/10/index.html?page=2St. Luke's - sanatorium. (For TB as well I believe
)
Berwick House (St Luke's) for the cases not able to be resolved (previously).
The original Hospitals in Dundas Mews (Houses converted) after an explosion in the Iron works (I believe)
Good places in their day.
I also remember the older Hospitals before the end of their day. Would sooner go to South Cleveland (come the day).
Regarding conservation of such places, the exteriors may have some merit, but the interiors were unusable for modern practice. So unless a use could be found for (in modern construction and all the environmental aspects) such properties, then redevelopment for the good of the community (although with future hindsight, perhaps not good) is or should be regarded as beneficial.
Don't get me started on St Hilda's area regards conservation - Lots of really ancient sites and from the early development of the area - all gone.
George