Some possibilities for you to consider on your weekend:

If you are in Chemnitz and rent a car, you might drive to some of the small towns in the nearby Erzgebirge mountains. They are famous for wood carvings, (" nutcrackers originated here, as well as the "smoker men" -)

Another possibility is to spend the weekend at either the Rennaisance or Marriott in Leipzig, just an hour from Dresden. The rates are very reasonable.. I myself prefer the Marriott. The old city is beautiful, there are many musical opportunities (the famous Gewandhaus orchestra, St. Thomas Boys Choir) and excellent shopping, as well as wonderful cafes and restaurants ( try to Coffeebaum, a restaurant in what was one of the first coffee houses in Europe 250 years ago).