I think more than any of these things, or at least as important as the issue of "woman's proper place" is the part everybody is forgetting... So many places of public education are scandalous occasions of sin. Who hasn't heard about the drugs and drinking (and dare I say, even 'hazing'?) and what have you going on in colleges?
Whether it's good for a woman as a woman is only one issue. Whether it's a serious occasion of sin (not the least of which may be the idea to embrace being a "career woman" instead of a housewife which would probably help her salvation more), is an equally if not more grievous point of the question.
Finally, even if you could find a place of 'higher education' where such things weren't going on (I'd be shocked if you could, but... for argument's sake) where can you find a place that isn't also riddled with lies being taught as truth, and students being forced to conform to those lies... eg, liberalism, evolutionism and the like... Psychology, for instance, in the light of God, the Father of Truth, is little more than a sick joke with all it's adherence to Freud and the like, with no regard for the reality of the human soul, and human nature which includes and is effected by that soul.
Many subjects, I'm sure, are riddled with this problem, and that's as relevant to men as women, I might add. Just what are you going to learn where God, and all truths pointing to Him, are forbidden? Since truth is a solid body, not a lot of parts that you can separate, and keep some apart from others, when you deny the very foundation of truth, reality and this whole universe, you can hardly expect any assumptions or theories based upon such a belief to be trustworthy, or true.
Even in the arts, one is faced with having liberal ideas shoved down one's throat, while greats like Dante are taboo to discuss beyond how horrific the inferno is (most students would say cool at best, but more probably 'boring'). You'll spend time studying modern poets and writers who touted liberal ideas, while Shakespeare is treated like an interesting antique.
There are greater problems with universities or colleges than merely should women attend them rather than stay home and be mothers. There are serious moral issues, and issues of what it is you will be paying to learn there.
When I was younger I used to wonder why it would be wrong for someone who knows the truth to read literature from other religions. As the years passed, I realized that at least in part it's because whatever we are exposed to will be planted like seeds in our minds, and there fester with the danger of sprouting into something very like a weed... deadly to any fruitful plants, and darn hard to kill. Having seen television rob myself (earlier in my life) and others around me of their moral scruples, I can attest to the fact that we're a lot more impressionable than we would like to think. The thoughts will be there, whether we want them or not. And if we hear nothing but those thoughts all the time, it begins to eat away at the roots of faith at a level generally well beyond our noticing or protecting against it.
I'd venture to guess most fallen away Catholics didn't get that way over night.