One of the various Canon "Digital Elph" cameras.

I've got one that's a couple years old now, which I've been quite happy with. Canon seems to keep updating this line in the obvious sorts of ways you'd expect (the new models are smaller and have more pixels) without doing anything to make them terrible.

From a quick look online, I see one of the new models (SD110) available for $160. That's for a 3.2 megapixel with 2x optical zoom.

They're small; not crazy james-bond small, but palm sized (3.4*2.2*1 in).

Uses a rechargeable lithium-ion battery. Good for at least 100 shots. (according to the official specs, 210 with LCD on, 550 with LCD off. they don't say what happens when you use flash, that's probably what gets you down in the 100 shot range) You can pick up a second battery so that you have a spare charged one. The li-ion rechargeable battery packs are pretty small, so it's easy to drag along if you've got some kind of camera case.

I don't know about flash recharge speeds... I suspect the only place you find super-fast flash recharge speeds is when you move to external flashes with a lot more juice. (capacitors only move so fast...)

One thing I like about my older model that I'm not sure the newer models have is the *very* solid feel of the camera body itself. One problem with really small cameras is that your hand always shakes a little and that can lead to blurry photos or slightly longer exposure times; a heavier camera body helps minimize that. The new one is, at least, a nice-looking metal body, though.

Shutter speed's kinda slow, though (1 second or so). I think you need to pay $$$ to get fast shutter speeds. (takes a while to move 10MB on a cheap bus)

And, of course, like all digital cameras, it comes with too small a memory card.

To be fair, if you get the SD110, a spare battery pack, a bigger memory card and well-made case to hold all three things, you'd likely end up above your declared price range by about $50. Without any accessories its in the middle of that range, though.