an Xbox controller is deeply foreign to her.
If you want to introduce a total newbie to the hobby, you do NOT give them games that involve full manipulation of a dual-stick controller or keyboard/mouse combo. Full-stop. They will become frustrated, they will give up, and they will be far less likely to try video games again at a later date.
You also do NOT play cooperative games where your vastly superior motor memory gives you a noticeable performance advantage. You shouldn't try to "compensate" for their lack of ability by "carrying" the two of you through. Your teammate isn't an idiot. They will perceive what is happening, and they will resent it.
My advice? Diablo 3 for Xbox 360. No 3D navigation, single-stick movement. Starts with literally one straight forward attack/ability button and slowly adds more mechanics (and buttons) as you progress. Introduces the concept of "background mechanics" in the form of stats and gear, but nothing overly complex. Highly scale-able difficulty, very little punishment for failure. Also playable cooperatively, and you can "sandbag it" a little without being patronizing. High production values help, too; great graphics and sound, serviceable story, awesome cinematics. I've personally deployed this game as an introduction to the hobby, and it really worked.
Not that I'm necessarily accusing the O.P of this but there's quite a condescending attitude pervading this thread treating women who haven't played games like they're fucking children and recommending stuff that is the gaming equivalent of Fisher Price (it'd be interesting to see if a male "non-gamer" would get this treatment).
My sister is very intelligent and a non-gamer. She loves batman. She loves puzzles. When her boyfriend bought a PS3 for Madden, I gave her Arkham Asylum and Portal 2. Based on her preferences, those games are no-brainer homeruns. She tried them both, immediately became frustrated by the controls, and never touched either game ever again.
Gamers generally take their motor memory and hand dexterity for granted. This obviously doesn't matter when you're playing a non-real-time strategy game or anything with a point-and-click interface (which is why this poster's gf had no trouble with Dragon Age), but when it comes to navigating a three dimensional space or rapidly pressing different buttons in response to on-screen indicators? Lack of experience with relevant input devices is absolutely a deal-breaker.
Now there is a very logical correlation between basic controls and shallow or simplistic content. If you can find a game that is complex/deep/interesting without frustrating a completely new user with input challenges, that's awesome. Unfortunately, with "basic controls" as your predominant criteria, the vast majority of games will be more simplistic/shallow. Recommending such fare doesn't make you prejudiced or sexist or disrespectful. It means you understand the initial limitations of someone attempting a new hobby for the first time, and you're making responsible recommendations with future growth in mind.