I agree, the tic tac toe game is pretty trivial to solve. The set of possible situations a player can face is very limited. And, as firstPerson mentioned, if you write a decision tree for the optimal strategy, it is very simple and unbeatable, that's too easy. Typically, to really be able to test any kind of AI, you need a scenario in which there are no unbeatable strategies, where even the stupidest strategy (usually random decisions) is expected to win at least some of the times, and where no simple strategy is optimal (in AI terms, the value-function is far from simple).
There are several such open-ended problems that could be fun to tackle. For instance, a while ago I took a machine learning course and people had all sorts of diverse AI projects to present at the end. The problem I did my class project on was a Pursuit-Evasion game. This is very simple to set-up, you just simulate a fast-moving, slow-turning pursuer and a slow-moving, highly-maneuverable evader in a 2D or 3D environment (just empty-space environments). Then you just get the pursuer to catch the evader, each starting at random points, and train both AIs to learn their respective optimal strategies, then count to number of successes of each party (if evader is still alive after X period of time, he wins, otherwise, well.. he's dead). I personally tested several AI algorithms on a slightly more complex scenario, and it isn't easy to solve (but luckily, …