I think it's rather difficult to find a camera that's small and portable, under $100, and still go take good quality pictures.

The only ones I know that are around the $100 range are the Canon A590 and A470.
I have the A590, and I must say that although it's somewhat big and bulky for a p&s, it takes pretty darn nice pictures. It has 8 megapixels, but I'm personally satisfied with that amount, haha. ~$110
I've never tried using the A470, but based on the reviews on Newegg, it seems to be decent, and it's quite small like how you wanted. It doesn't have a viewfinder, but I don't know if you're ever gonna resort to using it since it's got the LCD screen. It has 7.1 megapixels. ~ $95
These two cameras both use AA-size alkaline batteries. Try buying them online instead of retail stores if you're on a budget. Some legit ones I know are buydig, newegg, bhphotovideo, and beachcamera.
Oh my, what a long post. I have too much time on my hands.
I'm not that experienced with cameras, and I've only had a Canon before, but you can look into those 2 if you want. Good luck finding a camera!