We did ask our vets first thing if they could help us. But, they help out so many shelters and rescue organizations, so they personally do not take in stray animals.
We ended up taking it to a shelter about 45 minutes from here. All the Toledo-area shelters were full (and I haven't been too thrilled with them anyhow). I think we found a good shelter - It is no-kill, even if the animal is sickly. If they find something drastically wrong with the cat, they will call us first before putting it down - they will also call us to let us know when it gets adopted. I hate having to send any animal to a shelter (where it might live in a cage for the next year) but I have hope that it will have a good life with a family that will love it.