Machines said:
Mirrors Edge and the newest Prince of Persia game.
As a
long time girl gamer, I endorse this statement. Then again, I like violence in my stories. Rather, I like conflict. I'm sort of a weaver of story myself, and understand that a story without conflict is dull. However,
Prince of Persia [2009] is not the gory kind of violence that some of my girl friends would be turned off by, and contains just enough sexual tension between the Prince and Elika to get any one of them giggly.
Mirrors Edge... I personally love. I love that game to death. There's something about this game that inspires me, and fills me with productive, proactive energy. However, when I showed it to a few of my gal pals that are only casual gamers at best, they got motion sick very quickly. So before you buy this one
for her, ask her if movies like Blair Witch Project and Cloverfield make her ill at all. (A "Yes" reply means this game is out.)
Both games require a certain amount of eye hand coordination taken for granted by todays gamers. So PoP 2009 may be the one to get, since it's "Death" mechanic barely takes the player out of action for more than a second.
After flipping though my games, those are my Disk-based recomendations.
PixilJunk Monsters [PSN] is all kinds of addicting tower defense fun.
flOw [PSN] was free on the PSN over the weekend. Check to see if it still is. That one may be a winner too, though it lacks plot.
Flower [PSN] is alot like flOw, in that there's little to no plot, but in both cases, there's no violence, and they're totally artsy.
Dark Mist [PSN, Hong Kong]; this is a solid game. It's only available in the Hong Kong store (which takes US currency), so it'll take some homework to get it. It's like a mixture of Legend of Zelda (nes), and any cute Asian game.

It's quite fun, easy to get into, and challenging at later levels. There's an expansion that I whole heartedly recomend.
There are other games I'd recomend, but these are the strongest suggestions, I believe.