Brookfield Insane Asylum
This institution is where Lois finds her secret brother, Patrick, in S4E17, "The Fat Guy Strangler." The location pops back up in S14E3, "Guy Robot," when Peter, Quagmire, Cleveland, and Joe go there in search of Peter's old mattress, only to find themselves committed for various reasons. Except Quagmire. Quagmire just has sex with the patients.
There is no town in Rhode Island called Brookfield, but both Massachusetts and Connecticut have one, although as far as we know, neither has an asylum. If you're looking for a Rhode Island twin for Brookfield Insane Asylum, look no further than the long-closed Ladd School (1907-1994) in Exeter. It's the state's most infamous (historical) place for the shutting away of our differently-behaviored citizens.