Where can I take my cat where they won't put her to sleep?

You should take her to the vet and make sure she doesn't have a bladder infection before you just ship her off to a shelter. If a cat has some sort of bladder infection, it will avoid the litter box because it associates the pain with teh litter box. Do you keep your boxes clean - like every day or every other day, scoop them out? Do you have enough boxes for all your cats? The general rule is one litter box per cat, plus one extra. So if you have 4 cats, you need to have 5 litter boxes.

Be patient and don't give up on her just yet.

You probably won't have to give her away or have her put to sleep. Most cats with this problem just have a simple bladder infection and they need antibiotics. Once the infection is cleared up, she should start using the litter box again. They stop using the litter box because they think the litter box is what is causing them the pain they are in. So they try peeing on everything else to see if it won't hurt that time. Take her to the vet before you do anything drastic.

my friends cat did the same thing, they put it in a room with NO furnature or carpet and they put food, water, scratchy post, and TWO litter boxes and when the cat would pee in the box they gave it treats

If you're in the UK the Cat's Protection League won't put down healthy cats. One of mine came from them.

Petco/petsmart

GOOGLE "NO-KILL SHELTERS IN (YOUR AREA)" YOU WILL PROBABLY HAVE TO PAY FOR IT THOUGH.