I give knives to women fairly frequently. It's usually something they don't have, but always appreciate.
I usually give a Swiss Army (Victronix). For girls I give the small executive with blade, scissors, fingernail cleaner. For teenagers and single women, I give either Leatherman or a medium Swiss Army (purse size) with scissors. For married women, it's a Spyderco Q (you can still get them), serrated Delica, or a medium Swiss Army. Married women have access to tools, thus they don't really need the Leatherman and it can be lifted by the husband. Many people can't sharpen readily, thus the Spyderco serrated is useful, but Spydercos don't have screwdrivers or scissors, which many women like to have in their purse. That's why the medium swiss army is a good choice.
However, if your girl is an outdoors type, a Buck lite is often appreciated. Cheap, sharp and light with a decent size blade. One women, after seeing my Bear Balisong, wanted one for herself. I gave her one for Xmas. Not realizing the "history" of the knife, she freely uses it as a utility knife and now her neighbors (ex-cons) call her Blade.