Liverpool and Glasgow's reputations are based on old stereotypes that no longer hold water. Glasgow is the third richest city in the UK, but people on here seem to think it is one giant slum. The crime rate in 1/5 of Glasgow brings the rest of the place down. 'Murder capital of Western Europe' may be the case in some of the housing schemes deep in the east end, where there seems to be killings every other week, but for the third biggest city in the UK, the chances of getting murdered overall is only around one in 25,000. Take into account most people who get murdered are far from angels themselves, and for the ordinary person, the real figure is 10 times lower.
Liverpool is a fantastic city, I certainly prefer it to Manchester (although I might prefer Leeds to both to be honest), but I've family who live just outside it, and I would have no qualms about living there. It's very similar to Glasgow to be honest- both cities which were once amongst the best in the world, but suffered in the wake of post industrial decline, most notably in shipbuilding. Belfast is very similar in this respect. All three have came out of this era, and while it takes a couple of generations for these stereotypes to die, you can be assured Liverpool won't hold this rep forever. Nottingham was seen as one of the places to study, then after a rise in crime in the space of a year, people have shyed away again, which shows how fickle A-Level students are. Give it 10 years, and I'm fairly confident they'll both be back on the radar as some of the most desireable places in the UK to study in.