For those who take their care recipient to adult day care...where?

I’ve read that many caregivers take their loved one to an adult day care. Are these provided through senior centers, assisted living or nursing homes, hospitals? Curious.
I’ve been looking for one in our town and everyone says they don’t exist here. Respite care seems to be my only option. I'm wondering if any of them will take mom to their home. One more learning curve to go through.