2D platformers are a good start. Any Nintendo game really, especially the multiplayer games. Mario Kart Wii, New Super Mario Bros. Wii, Kirby's Epic Yarn, and Donkey Kong Country Returns. (Be warned, Donkey Kong is pretty damn hard) all come highly recommended. Wii Sports works too, of course.
If she's a diehard Disney fan, get Epic Mickey. There's some pretty obscure Disney stuff in that one.
On the virtual console, get Chrono Trigger.
As for the 360...no FPSs, fighters, or portal? Is Fable 3's co-op local or online only? Sonic and Sega's All Stars Racing with Banjo Kazooie (awkward title) is a fun racer. It's basically Sega's Mario Kart, but it plays just as good (some say better).
Ps3...I don't have one, but LittleBigPlanet is the obvious choice from an outside viewpoint.
Check out any digitally re-released classic. I suggested Chrono Trigger earlier, but there's plenty that would work for a first-time gamer.
