All sugestions people are posting here are great. But since you will have limited playtime, start out with Mario Galaxy, No More Heroes, Zelda: Twilight Princess and No More Heroes. I haven't played Fire Emblem: Radiant Dawn yet, but reviews say it's better than Fire Emblem: Path of Radiance, which is the most involving story I played in a videogame yet. If your cousin has a gamecube controler and a gamecube memory card, I would certainly recommend you try that one also (the wii one is a sequel to the gc one).
Other than that, anything I recommend (almost) anything on my playlist. That Quantum of Solace game is average. And you want something different, anyway. :)
EDIT: Ohh yeah... if you like soccer games and want something different, give PES a try. Different than anything you played before. Damn... two months is not enough :P
