Dresden is a great place to visit. I assume you are young so stay in the Neustadt area.
Hostels in Dresden Neustadt
I 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.