Co-op Games!

terraria, dead island epidemic, l4d, castle crashers, killing floor, borderlands2, portal2... and sex.

Trine 1 & 2 or Orcs Must Die 2

I'm also getting my girlfriend into video games, here's what we've been playing (both coop and pvp): Battleblock Theater, TowerFall Ascension, Sonic All-Stars Racing Transformed, Castle Crashers, Jamestown, Ibb&Obb, Foul Play, Ultra Street Fighter IV, Divekick.
As I've mentioned she's quite new to "modern" video games (she used to play NES and Megadrive/Genesis games and lots of Warcraft III back in the day), but she's been performing quite good! Once she improves we'll try stuff like Nuclear Throne, Spelunky, etc...

Battlefield 3 and 4 to!!! kkk

so local co-op?

besides the already mentioned Trine series... some possibilities:

Rayman Origins
Lara Croft and the Guardian of Light
Jamestown
Hammerwatch (currently bundled)
Battleblock Theatre
Castle Crashers
Monaco
Adventures of Shuggy

Portal 2 would be good if you have two machines and can get two copies

I'm actually kind of sad, I had just made a category in my library called Local co-op/hot seat but it somehow got deleted so I can't handily check that to give you an extensive list.

You can find a lot of suggestions on the previous 123456 threads about the same.

Terraria
Unepic

Not sure there is a local coop, but they don't need a big pc

Don't Starve will come CO-OP, i think it's great idea!

http://www.steamgifts.com/forum/search/co-op
http://www.steamgifts.com/forum/search/coop

Commandos 2

Dungeon Defenders.

i do have the same Problem - just it´s my boyfriend who´s not into gaming that much. Things we tried and which i think are not too hard for a beginner:

ibb & Obb;
Orc´s must Die 2 (but i´m sure you´ll need a second PC for that, but wasn´t a prob as we have two);
Portal 2 (same as with OMD2);
Castlecrashers
Monaco (i played that with friends but i think it would be easy - nice music by the way)

Lara Croft and the guardian of Light is a great game, but i think it´s not for an absolute beginner.

Trine 1 and 2, Magicka...

PixelJunk Monsters Ultimate and PixelJunk Shooter have nice local co-ops.