One thing that I remember getting me pretty excited back in school when we learned PASCAL (a few years ago...) was to write a simple AI for a very simple board game, Connect Four in our case. It's ideal because you only need text input/output and have the real game set-up next to the computer. Connect Four is great because you need some strategy but the moves are very simple. The AI part isn't difficult - you just need to come up with some sort of scoring scheme for the situation on the board at the end of the move and, if there is time to make it more complex, maybe all possible outcomes of the opponents next move.
Another thing I would suggest is screen scraping web sites - maybe some script that gatehrs information about the next show of a TV series?