May I make an alternative recommendation?
I started sending little digital cameras as gifts to young nieces and nephews a few years ago (those keychain cameras), and I realize quickly that they are more interested in taking videos than snapping pictures. I also find that the little ones don't really care about optical zoom and image quality in most cases (mostly view on computers, so anything 2-3MP will suffice).
An inexpensive "digital camcorder" with still picture function (aka. "hybrid camera") is Aiptek:
The price of the lower models is well within your budget. The advantage over mainstream digital cameras is that, it saves the video in MPEG4 format, which is much smaller in filesize than the common MJPEG video format of digital cameras (eg. up to 1 hr+ (depending on strength of compression) per GB of memory card for MPEG4, compared to only 10-15 minutes per GB for MJPEG). True, the video quality MPEG4 may not be as good as MJPEG (unless the video bitrate setting is at the highest, in which case the filesize also increases), it is not that relevant to our young videographers.
Buy a 1 GB SD card to go with the Aiptek and they are happy campers!