Online Gaming for Couples?
I can see your girlfriend not being into the typical games such as Counterstrike or Quake3. Most women don't like the killing. However, why not try an MMORPG such as Everquest, Horizons or the like. They give women the social aspect that they're looking for and add some excitement into the mix. I know many couples that play Everquest as a couple and in fact am currently using it, combined with the phone, to chat with that lady who is on the other side of the country. It gives you something to talk about on the phone as well.
Just make sure that you're carefull with it. Give her the option of trying it and make it low key, or else she might feel put off by this new communication medium.