Dresden is a great place to visit. I assume you are young so stay in the Neustadt area.
Hostels in Dresden NeustadtI recoment (and another TT member too,
Mondpalast, it is right in the centre of the party area.
The Neustadt really comes allive at weekends, it is a bit quieter during the week.
Cross over the river to the Altstadt and spend a day wandering around all the Baroque buildings. Therei s an information office at Theaterplatz
It is is a nice day I recommend going up the tower of the Frauenkirche (a bit costly, 8 or 10 Euros) but fab views of the entire city.
After that it depends what you are into.
some are:
Old masters picture gallery
Porceling collection.
Mathematical and Physics musuem
Green vault (but you need approx 6 months prior booking to get in there!)
New masters gallery
Transport museum.
Semper opera
Zwinger
and that is only a fraction of what there is.
P.S. If you are coming from Belrin the train stops in Dresden Neustadt first and then to the main station.