Right, a few things.
Glasgow has a problem with sectarianism for those who give a toss about it. In my 8 years in Glasgow's west end I saw one march, and in my ignorance of what was occuring, I thought it a rather pleasant and peculiar thing. In general, in the west end, but really throughout Glasgow, you will not have a problem with sectarianism. Once you move you'll see what I mean, its a non-issue.
Glasgow's charm comes from its imperfections - graffiti, rougher-seeming bits, etc. Furthermore, even in a more run-down area, like Maryhill, you're still perfectly safe. TBH, I'd rather live in Maryhill than Anniesland. Maryhill's got good bus links into town, is easy walking-distance to the park, the Kelvin walkway, the tube, plus it's got a massive Target-like Tesco. But anyways, in general, living in a visibly more run-down area in Glasgow is not equivalent to something similar in the states, at least in my experience.
Rereading what she wrote, she's got the boundaries right for my preferred living areas in Glasgow west-end, but re not feeling safe, I just can't settle with that. Glasgow is rough, as aforementioned, but its safe - so outside those boundaries might look less desireable, but there is nothing wrong with them, there's no sense of the 'wrong side of the tracks', its just a place where people with less money live.
When you're looking at crime, make sure you research violent v nonviolent crime. The population in Scotland is generally less segregated - unlike many areas in the states, so you'll live only a street or two away from people with less money, less education, less favours in life. This may mean some crime in your area, but not crime that will necessarily affect you - like shoplifting, drugs charges, fighting, etc. I'm no expert, but its something to consider.
So, onto the hill, and walking. The clue is in the name, Hillhead. The university is on a hill, so there's no getting around it. Also, its dark quite a large amount of the time in winter here, so your (presumably adult) daughter will be walking alone in the dark quite a lot of the time. I cannot stress enough how much this will not be a problem in Glasgow's educated, wealthy west end. I would feel, have felt, do feel safe most places in Glasgow, most times of the day. Same as any major city.
I'm guessing you won't be moving into typical student housing, which, if its anything like it was in my day, were large tenement flats with IKEA kitchens, cheap carpeting and bare bones furniture. It'll be two different markets, you and the students, so don't worry about them. Look on rightmove, see if its available at the time you want it, click the button for 'contact an agent' (or whatever it is now) and they'll get back to you with a time for viewing. Simple as that. If you like it, and no one else does, you'll get it. Keep looking and see if you can be the first to view it, and then to ask to let it. I would, however, in the meantime, see which letting agents are letting the types of flat you like, and get in touch with them to see what the requirements would be for someone in your situation to rent. Stress your independent wealth, etc - 6 months rent upfront would not be a problem. This will be important, as you may find a perfect place, and they may be perfectly happy to rent it to you, but if you don't tick the boxes, they'll just rent it to the next interested person, of which there will be many.
Right, a bit bust just now so I'm not going to reread this for typos - best of luck and get in touch if you need any more info.
Cheers.