a cat who is ill in some way will hide. My brother's cat hid so well he could not find her for three days. He went nuts looking all over the place for her outdoors and she actually was inside. It was the same plan as yours--take her to the vet the next day. He eventually found her drinking water near the drain in the basement (yuck). Maybe you should leave some water around in a few places.

I had a cat that was ill, too, and found a place where I could not find her. Really scared me.