For anyone researching in New York State, I just found that Ancestry has added a New York Death Index. This covers areas outside New York City, and finally is another source besides FindAGrave and newspaper articles for NY state deaths.
The source is:
Ancestry.com. New York, Death Index, 1880-1956 [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2017.Original data: NY State Death Index, New York Department of Health, Albany, NY.
I have found both my grandfather and his father; details include the city or town of death, as well as name, date, death certificate number. Neither of their wives were found. This helps as you must have the exact name, location and date, as well as $35, for each death certificate you want a copy of (even uncertified for research).
Edit: source was added to Ancestry on 31 Aug 2017
