Cat-loving residents get the pleasure of holding and stroking an appreciative furball -- and possibly to hear and feel the phenomenon of purring. (Purring is one of the things cats have over dogs. And it just might allow you to steer the conversation to the Creator, since secular scientists are still mystified by this uniquely feline capability.)
Your cat gets to enjoy lots of lovin' from someone who is not in any hurry to end the session.
And you get the pleasure of making some old people very happy.
If this sounds like a good idea to you, why not give the Activities Director of your nearest nursing home a call to explore the possibilities?