The Neustadt is really under-rated - so cool and lovely to visit, especially for students. Also if you can get a look in at the yearly Stadtfest in August, that is really worth visiting. You can easily do this city in a couple of days as it is quite small.
Insider Tip:Try and get a map written by students - it gives some really good information about what is/isn't worth seeing, especially on a budget! These maps are available in most hostels.