General:
* Sick bay
* Hospital (though this is generally a larger facility)
* Clinic
* Medical center
* Treatment center
* Dispensary
* First aid station
More specific:
* Nurses' station (if referring to a specific area within a hospital)
* Ward (if referring to a specific section for patients)
* Rehabilitation center
* Convalescent home
Informal:
* Sick room
* Sickhouse
The best synonym to use will depend on the specific situation and the level of formality desired.