Without really knowing anything about either of your personalities or tastes...
-> The Walking Dead: Season 1&2 - An excellent experience with multiple people regardless of whose at the controls. If you've played before then let her make the decisions.
-> Hearthstone - Simple to pick up and play allowing for plenty of creativity and co-operation.
-> Portal - A great introduction to FPS style games and their controls with a very friendly 'tutorial'. Obviously Portal 2 is a great follow up for the co-op experience.
Basically any game that doesn't require twitch based reflexes and really eases you into the experience. There are plenty of games out there that offer insanely forgiving difficulties as well. Games like Mass Effect 2 or Diablo 3 might seem overwhelming but mechanically they build up slowly. This isn't like teaching your parent how to use new technology they've never seen. Your girlfriend is likely to pick up these things quickly if it interests her.
-> The Walking Dead: Season 1&2 - An excellent experience with multiple people regardless of whose at the controls. If you've played before then let her make the decisions.
-> Hearthstone - Simple to pick up and play allowing for plenty of creativity and co-operation.
-> Portal - A great introduction to FPS style games and their controls with a very friendly 'tutorial'. Obviously Portal 2 is a great follow up for the co-op experience.
Basically any game that doesn't require twitch based reflexes and really eases you into the experience. There are plenty of games out there that offer insanely forgiving difficulties as well. Games like Mass Effect 2 or Diablo 3 might seem overwhelming but mechanically they build up slowly. This isn't like teaching your parent how to use new technology they've never seen. Your girlfriend is likely to pick up these things quickly if it interests her.