American Horror Story's hotel isn't based on a particular real-life establishment. It's a fictional construct that embodies the dark and creepy themes of the show. The showrunners use their imagination to build a hotel that fits the horror narrative they want to tell.
American Horror Story often takes inspiration from various horror elements and combines them to create its settings. So, it's not directly based on a single existing hotel. The show's creators craft a unique and terrifying hotel concept for the storyline.
I don't think it's based on any specific real hotel. It's more of a fictional creation for the show.