There are several sites with refurbished or reconditioned cameras, but SSQ said to avoid them like the plague! We've seen a couple that are very small, but Clare has long fingers, and she's always worried about sticking her finger in front of the lens all unawares. ;o) We'll find something, but prices sure have come down in the last couple of years. You can get a 3 or 4 megapixel camera for less than $250 these days!
When I really start looking seriously, I'll be trying to keep it under two hundred...maybe even close to a hundred. I don't need anything fancy! I figure my best bet is probably finding a place that's getting rid of an older model that's being replaced.
And I know what you mean about the size. I've used a vey tiny Canon before...an Elph? Something like that. Sure, it was easy to carry, but it was darned hard to hold onto, and hard to see what you were doing, too. I'll take ease of use over small size any day.