Welcome to Wiichat! =)
There're two Zelda games for the Wii; Twilight Princess and Skyward Sword. You should definitely get whichever one ya don't have.
Mario Kart Wii (if this isn't the game that came with your Wii; some Wii can come with MKWii, some with New Super Mario Bros.) is the premier racing game on the Wii, and it's damn-fun. Your girlfriend would probably enjoy it too.
One of the best action games for the Wii IMO, is Red Steel 2. It's all 'bout wicked swordplay, as well as guns if you're into that too (you can go through the entire game using your blade alone if you wanted lol). But unlike a lot of games, Red Steel 2 fully utilizes the Wii Remote's motion controls. Really fast paced and epic combat-oriented gameplay.
Just don't bother with Red Steel 1 though, really poor game that doesn't resemble 2 at all... The story lines aren't connected anyways.