I like The Sims, and some of my girl friends like it as well. I think that stems from the whole barbie obsession as a child.
I can try to give a few suggestions as to what I like and consider girl-friendly, and what some of my friends play.
Every person is different though, one of my girl friends likes horror games, like Alone in the Dark and Resident Evil. Another one likes Grand Theft Auto. Another friend loves adventure and puzzle games. And then there are those who ONLY play Sims and Solitaire. So that could be the case, don't get your hopes up just yet.
Sports games are also great, think tennis, Tony Hawk skateboarding, Soccer, Need for Speed etc.
And then ones I think are fun, but not everyone agrees, are point and click adventure games, or hidden object games. There's plenty of them and they are quite cheap.