My mother came to live with us because she had Parkinson's disease (which also carries the risk of dementia). However, she was quickly diagnosed with Alzheimer's (something both her mother and brother had).
My dear husband had a house built to accommodate my mother, and we cared for her for three years until my mother's physical health and Alzheimer's reached a point that she needed 24-hour professional care.
Our gerontologist helped us find a lovely, caring nursing home that was very home-like. She stayed there for a while, and then requested to be moved near my brother because he had grandchildren.
She is there now. Unfortunately, the facility isn't as nice as the other one. She is happy because she sees her grandchildren, although she is starting to not remember names; she simply loves the visits.
It's very, very difficult to care for someone with Alzheimer's, but I was very lucky to have a wonderfully supportive husband, good friends who helped out, and a very supportive church family who helped and even visited my mother regularly (at our home and at the nursing home).
I consider that time with her a blessing because I was able to do for her as she did for me, although it wore out both my husband and me to the point of pure physical exhaustion. I would not trade that time of caring for her for anything.