The neckline letters were always the initials of the medical facility where the nurse trained and/or worked. I agree that it was likely "something" General Hospital and it may be quite impossible to pin down further... S is such a common letter for city names. Googling SGH produced many possibilities.
I've read that the yellow lining may signify a lead nurse or nurse manager, but it seems that may just be an internet theory and it may really be that each facility simply chose what colors they wanted to use.
Nursing capes were most commonly worn in the early- to mid-20th century.
These people may be able to give you more definitive information:
Welcome to the Museum of Nursing History located at La Salle University!
nursinghistory.org
The also have a FaceBook page: The Museum of Nursing History, Inc.