$1,000 · apartment, cottage, suite for November 1st

I am a young senior woman, with great references,credit, pensions and working part-time. I am looking for affordable, quiet suite to call home. Would like to sign a lease and also have a full kitchen, access to laundry, as well as bath tub. I am looking for October or November, month is flexible. I do not have a pet, but would like to get a cat again, however this is not a deal breaker if I can find the right place.