in case you didn't know before, chemnitz is the place where the former riches of saxonia were worked out. leipzig the place where they were sold and dresden the place where they were blown away (especially by saxon kings & co.). when a tourist, i would highly recommend to visit dresden and its nice city center with all that palaces, churches, galleries, castles (e.g. castle pillnitz), will you?
in case you are fan of industrial chimneys, chemnitz is the place to be :o)