The New Orleans Public Library has Charity Hospital admission books 1818- 1899 and Charity Hospital death records 1835-1894 on microfilm. A hospital death record of your ancestor, if one exists, may provide his burial place. Refer to the following link:

http://nutrias.org/~nopl/guides/genguide/hospitalinsanity.htm

Charity Hospital has a cemetery which was established in 1848 for the poor of the city. The monument at the cemetery reads:

"This cemetery was purchased by Charity Hospital in 1848 and was originally known as Potter's Field. It has historically been used to bury the unclaimed from throughout the city including the victims of several yellow fever and influenza epidemics."

A photogragh of the monument and the entire inscription can be found at the following link:

http://www.flickr.com/photos/hipbone/4031356524/

A few Charity Hospital admission records have been placed online at the following link, but the online records unfortunately do not include any records for the 1860s.

http://www.usgwarchives.net/la/orleans/charity.htm

Regards---