What is the best housing arrangements for a person with dementia, who is not going through the anger, yelling stage?

Nursing homes accept Medicaid.

Some Assisted Living Facilities do accept Medicaid. Some accept it after a period of self-pay, and some do not accept it at all. Find that out before you bother with a tour.

Yes, he can get to and from the dining hall, but also what about the cost? He only has medicare/medicaid and a disability check.

Assisted Living will take wheelchair and power chair candidates. He has to be able to get to and from the dining hall without getting lost. Go on some tours for places nearby.