I am a girl (a gamer, but nevertheless a girl), and I do not like playing shooters or zombie killings for prolonged periods of time because the graphics are quite dark and grainy, and things jump out at you and you then have to take a lie down, a general lack of spacial awareness, I cannot shoot straight and then I just get bored after being shot/eaten for the umpteenth time.
I am more a Nintendo person but the games I really enjoyed on the PS2 were Kingdom hearts, final fantasy and ookami. Since your girlfriend likes sims, maybe this shows that she likes the human element of games more than fighting or shooting. They also had pretty graphics, a good story line and were compelling. I realise that they are single player games, but you could always take turns. I also really enjoyed guitar hero because I could listen to music and press buttons at the same time, which is quite addictive. I think you can do multiplayer with guitar hero as well.
I think that when it comes to more `family fun together` games, the wii is the best shot with games like mario karts and wii sports because most people, beginner or advanced, can play them and have fun. Maybe you could rent one from your local store.
Best of luck to you
p.s. apologies to all the girls out there who are actually good at playing games. I am not implying that girls are rubbish at shooting games and the more `serious` `hardcore` genres, I just happen to be myself.