Hey mate. I live in Ilkley (you may have heard of Ilkley moor and the cow n calf etc etc (I won't sing the song), a very affluent place about 15 miles NW of Leeds and about 12 miles NNW of Bradford. Anyway I'll get to the point. The stereotypes the north suffers (especially the very cosmopolitan county of West Yorkshire) are usually very wrong and people from the south often have a very negative idea of the place. I myself am originally from Maidstone, Kent so I feel I am qualified to say such things.
I have lots of friends in the city and its suberbs and of course some suberbs are rougher than others (Harehills, seacroft, chapeltown) but this is the same in every city in the country. I go out into Leeds all the time and have done for many years and I have never come across any trouble night or day. The areas in which you will live whilst at leeds uni are great areas with one of the biggest student populations in the whole country. They contain lots of green areas and the great thing is being in Leeds is you can enjoy the positives of urban life in and around the city whilst only being a few minutes train/bus ride into some of the most tranquill and beautiful countryside in the UK. I know we're young people and we like the hustle a bustle of fast paced city life but theres nothing like getting away from it all for the day and you can really do that in Leeds unlike many cities in the UK.
Although I live near to Leeds already, I am going to study at a Leeds uni in september just because I find it such a great city with such a good atmosphere and lots of character. And lets not forget the excellent nightlife, shopping an dining out that the city has to offer! And you mention Bradford, well Im not a huge fan of Bradford but then again I don't mind it, the place certainly has character and Ive never had any trouble there. True it does need alot of work doing to it but this is already happenning and sometimes it just makes a change from Leeds everynow and then, especially if you want a decent curry which i frequently do. Leeds and Bradford are about 10 miles appart but I find it amazing how different the two places are. Bradford isn't a great city like Leeds is now but that doesn't make Bradford a terrible place to be avoided at all costs!
Hope this helps at all. Tom