Is there a good .22 pistol for less than a hundred dollars?
That is a pretty good challenge. It would probably require you to go used, and then one of the lower cost but still decent revolvers such as the H&R or High Standard Sentinel, Iver Johnson Viking etc.
With one of these guns you will get pretty good accuracy with good but not excellent fit and finish. Trigger pull will usually be fairly poor on double action (if it has that feature) but OK on single action.
There were some decent cheap .22's made by Jennings, Davis, etc. I had a Jennings and was really surprised at it's accuracy. It was also reliable. On the down side, it was constructed mostly of pot metal, and had poor sights and trigger.
You just might find a Ruger single six in fairly rough shape, but still functionally perfect.
I bought a Hungarian copy of the Walther PPK (FEG) and actually like it better than my real Walther. It is just as accurate and more reliable. It cost just a little over $100 tho, but not much more. I think it was something like $129, but many dealers try to get over $200 for them.