I suspect that the "town" you are looking for is Sanator, but it is in the southwest part of South Dakota. It isn't actually a town, but mostly the old sanitarium. Sanator is several miles south of Custer, in Custer county. Your g/grandmothers death should be registered in the books in the courthouse in Custer.
I don't know if there would be anything on this site but there is a SD Department of Health site, http://www.state.sd.us/applications/PH14Over100BirthRec/inde...
. This will get you their "100 year old birth records" page but you can check their links for other stuff.
I would suggest googling the word Sanator to see if you can find anything there. And, you can ask the Custer library to see if there is a historical society or something kept in their holdings about Sanator.
The setting around Sanator is spectacular, with mild weather and tens of thousands of evergreens on lots of hills. But, I suspect that in 1919 your g/grandmother probably sat in her room with the drapes drawn tight. Sad.