My brother lives in Leipzig for almost 7 years now and I will go there next month. I have visited him on several occasions but never stayed for more than couple of days. This time will be different since I will be there for almost a month. What things beside sight-seeing can you do in Leipzig? I would just want my time there to be interesting.
Well, I do not know if you consider a visit to a Zoo sightseeing, but that place is something worth seeing at least twice in those 30 days you'll be in that town. It has state of the art cages that allow you to experience Zoo in a way you have never before. As for other things, I guess you already know there are many nightclubs and cafs that would make each of your evenings there very interesting.