These two, specifically The Last of Us.

The story heavy ones are a good idea.

Or some puzzle-heavy game that she can help solve.

But I think the horror game idea was the best. Play Amnesia with her and make sure you get scared together.

Any game YOU want to play. That's the game you should play in front of anyone.

this one of course

http://youtu.be/H0q3qcLkw1A

Animal Crossing. My relationship with my GF only got better while playing this game. Of course, she played along as well once she really started getting into it.

Grandia 1 or 2 and Lunar 1 and 2 the stories are so interesting and engrossing that i think it would be enjoyable even for someone to just watch, and those games also have great pacing.

Rapelay, Manhunt, Killer 7

Just because I'm playing it and everyone should play it: Shovel Knight.

She'll love you for your classic taste (8-bit art style and music lets her know that you appreciate the classic things in life) and your expert gaming skills (as the game is also notable for its 8-bit difficulty).

Steel your shovel D21Lewis, for adventure awaits!

Mario Kart

Frog Fractions