My mother has limited vision and is not real stable on her feet. Where shall I look and will Medicare pay the bill?

If you are asking about assisted living or nursing homes, Medicare will not pay the cost of living there. If her income is very limited, and she qualifies for a nursing home, she could likely go on Medicaid which does pay for nursing home costs. Otherwise, she would pay out of pocket until her assets are low enough to qualify for Medicaid.
Medicare will pay for a limited time in a nursing home if someone goes to the home from a hospital or under doctors orders (in some cases). Your state laws also figure into this. I'd check with her doctor for advice.
Take care,
Carol