The Morgue is located in the building of the Office of the Chief Medical Examiner (OCME) in New York City. Medical Examiners who work in the morgue include Dr. Eugene Hawes and Dr. Grannis. Sherlock Holmes has a standing agreement with Dr. Hawes in which they play chess and if Holmes wins, he's allowed to examine the cadavers. Its first appearance is in the Season Two episode "Solve for X".
The morgue consists of a ramp, examination tables, body cooler chambers, several offices and an elevator. In February 2016, a bomb was placed in a murder victim's stomach which exploded in the body coolers, killing OCME staffer Nicky Slater and injuring Dr. Hawes. ("Down Where the Dead Delight")
Watson in the morgue.
Holmes, Watson, Bell and Hawes.
Hawes and Nicky Slater.
The motto above the elevator in the morgue is "Taceant colloquia, effugiat risus. Hic locus est ubi mors gaudet succurrere vitae" which translates to "Let idle talk be silenced, let laughter be banished. This is a place where death rejoices to teach those that live."
The morgue was rarely seen in Season One, wasn't in the OCME building and was substantially different from the morgue in all subsequent seasons. ("M.") The first person seen in the morgue in the OCME building is Detective Bell who tells Holmes they've found the body of mathematician Cyril Nauer. ("Solve for X")