my 81-year-old mother has lost her spouse and lives in a different state. My sister and I want to move her here but she knows no one but me. What do we do?

Without knowing your moms state of mind, health, or really anything else I'd ask, why not? Why not move her closer to you? What's the problem with that? So if she doesn't know anyone else, wouldn't she rather be close to her daughter than to whatever friends she has left?