Although I haven't personally played it, you might have a look at 7TV rules as well - I've seen a few game reports that made it look pretty intriguing, and the focus is more... uh, well,
like a TV show in a series, rather than the latest modern Hollywood AAA summer blockbuster. In other words, there are narratives and side-stories that may not involve combat, but there are also rewards for doing fun cinematic things too. Rules are also apparently *very* easy to pick up.
And as much I love Necromunda and have a real
nostalgia for it, I really wouldn't recommend it for your purposes (nor Gorkamorka for that matter) - waaay too convoluted, and the mish-mash of badly-balanced rules is a pretty difficult sell to somebody who (1) isn't already a wargamer, or (2) isn't *really* into the setting and wants to spend the effort learning about it.
If it doesn't
need to be sci-fi, you might also have a look at Malifaux which is nominally Steampunky. It's pretty simple to play, the rules are clear, all models have a card with their stats and skills on (makes remembering things easier), and is more "gamey" than just killing-everything style games. The missions and factions have rather a lot of narrative/character too, which combined with the modest play area (3' x 3') makes it pretty accessible for newcomers.
You will probably need the official models (maybe 6-10 per side) unless you are willing to photoshop your own cards, or you have models that are similar/obvious enough to remember who's who during play. Finally -and this is purely anecdotal- it does seem that Malifaux has quite a few female players compared to other "big" games systems that I've ever come across... The core rules (i.e., everything apart from models stats) are free as well if you fancy a look first (
link).
Ask her... don't ask us. We think like guys, just like you. She might just want to go to the park and hold hands and walk around a bit.
Good advice in general. Mind you, I imagine that if she's already expressed some willing to play games, that it would be hard to articulate
what exactly without some prior experience (which in turn rather defeats this thread in the first place...).