During a simulation in 2153, Jonathan Archer implied to Degra that an infirmary had been at a Xindi-Insectoid prison colony where they had supposedly both been imprisoned. According to Archer, he had been lying in the infirmary when he had realized that there was little point to conflict which existed between them. (ENT: "Stratagem")
The infirmary was the primary medical facility aboard Deep Space 9. Located on the station's Promenade, in the central core, the infirmary was run by the station's chief medical officer, Julian Bashir, with a support staff of Starfleet and Bajoran medics.
During the Cardassian Withdrawal in 2369, the infirmary was heavily damaged and looted of most supplies. (DS9: "Emissary") Due to its relatively low security, it on occasion was the target of thieves and looters, including the Lethean Altovar, who attempted to steal the infirmary's supply of bio-mimetic gel. (DS9: "Distant Voices")
After she was injured by a Pah-wraith which possessed Gul Dukat, Jadzia Dax was rushed to the infirmary. Dr. Bashir was unable to save Jadzia, but was able to save the Dax symbiont. (DS9: "Tears of the Prophets")
Toward the end of the Dominion War, Bashir spent many hours in the infirmary, desperately trying to find a cure for the morphogenic virus that was killing Odo and his people. (DS9: "Tacking Into the Wind")
Background information Edit
Shots of Production Designer Herman Zimmerman discussing the creation of the infirmary aboard Deep Space 9 can be seen in the DS9 Season 1 DVD special feature "Deep Space Nine: A Bold Beginning"/"Designing Deep Space Nine". The set was built on Paramount Stage 17 as part of the Promenade set.
Regarding the holoprojection system installed in "Doctor Bashir, I Presume", Ronald D. Moore commented, "The unit was installed by O'Brien specifically for Dr. Zimmerman's work and was presumably removed when he left the station [....] I will rule out having an EMH on the station." (AOL chat, 1997)