I was born in and have lived in Glasgow for 22 years. I've been here for my entire University life. I would wholeheartedly recommend it. This is an amazing city which - if you're sensible, responsible and mature enough - can lend itself towards an incredible University experience.
The honest truth is that there are some issues within the city, but those aren't typically confined to the area in which the University of Glasgow is situated. The west end is vibrant, easy going and really quite safe. Personally I think this place get's an unfair amount of criticism on the basis of sectarianism, drugs, alcohol etc. These are all things which were much more closely related to the 1990s. The city's changed a lot since then, for the better. Plus, anywhere you go there's going to be bad people. Glasgow is no different. You very quickly learn how to avoid them.
My only word of warning would be don't be an idiot. It'll apply equally to wherever you go but there are just certain things you shouldn't let yourself do here. For instance - don't walk home late at night if you're on your own, especially if you've had a few beers.
The best way to see for yourself is to visit Glasgow, if you haven't already. The university is lovely and the surrounding area is very student friendly.