Directly located at the central station there's the club "Meilenstein" , they play house, techno & r'n'b. Quite good, though quite expensive as well.
At Dießemer Straße you find two clubs, "Schlachthof" and "Kulturfabrik" which have moderate prices and moderate alternative pop/rock music, depending on the day you get there. At Kulturfabrik (KuFa) you can also see gigs by bands of many genres.
In the city centre you can find Jazzkeller , providing Jam Sessions, Jazz concerts or just parties.
There are many teenager clubs as well, but I don't think they are of any interest for HC members who usually are older than 20.
You can find many bars throughout the city centre, I can recommend Anjuna Bar at Anne-Frank-Platz.