However, it's important to note that "hospitality" doesn't directly refer to the physical building or institution. Instead, it refers to the quality of being welcoming and generous to guests or strangers, which is often associated with hospitals but not exclusively.
If you're looking for a word that specifically refers to the concept or idea of a hospital, there isn't a single perfect word. You could use phrases like:
* Healthcare
* Medical care
* Treatment facility
* Institution of healing