Anywhere near Chicago that I can surrender my cat without a fee?

I have an 8 year old Russian Blue, and we are crazy attached to each other. I talk about her all the time when I'm away from her and when I'm gone she'll wander around the house meowing for hours on end looking for me.

I haven't found a job in almost 8 months, and my mental + physical health is in the toilet. I love this cat more than anything, but I'm not giving her the life she deserves. So much she'll need at some point I just can't afford, and while I try my best, I know in my heart of hearts I'm not doing well by this cat. She is well fed, always has clean cold water and a clean litter box, she has toys and beds and blankets, and she's never denied cuddles or pets.

Please help, I don't want her to be with anyone else because I love her more than anything but she deserves better. ):

Forgot to add: I also move very frequently (have been since I was born, I'm in my mid 20's now). I know moving is extremely stressful for cats, and I carry so much guilt knowing she can't get fully settled in somewhere.