To run one 125 volt/15 amp /1875 watt air conditioner for 19 hours you will need a minimum of eight batteries; you need 12 batteries total for the required reserve. To keep these charged you have to have a minimum of five hours of sun per day. This alone will require 70 solar panels (1,000 square feet of panels); because of the continuous draw on your batteries the life expectancy will be cut in half, so you will have to replace them approximately every four years. The cost is going to be approximately $354.00 per month for one air conditioner for 20 years. This doesn’t cover maintenance and battery replacement.
If you want to live off the grid like a hermit, go for it. I don’t know what you are going to cook with unless you use carbon emission products; you certainly can use solar to dry your clothes on a clothesline and you can use solar to heat your water and take a warm shower during the summer. Or you can use the creek for taking a bath (without soap, you don’t want any yellow-legged frogs to mutate).
I forgot to mention you can have your installation subsidize, this will require your friends and the rest of us taxpayers to pay for it; if that doesn’t bother you go for it.