Just north of city center is Melbourne University, located in the district of Carlton. With the hefty size of its student population, it only makes sense that an avenue like Lygon Street would arise to meet their needs. You can expect cafe culture to be at its pinnacle here, led by the impeccable and always packed Brunetti, although there are a ton of other possibilities in the surrounding area. As far as nightlife, there are a scattering of bars here and in surrounding streets, although the cool kids head about five blocks east to Johnston Street, where dimly lit rooms like the Old Bar are en vogue. Then again, don't leave Lygon if you want pizza, Italian, Asian, and much more.
If you want to hang out with the student population any day of the week, then Lygon is your premiere destination.