Saxony is the southeasternmost state of Germany. It borders Poland to the east and the Czech Republic to the south. Along the Czech border are the Lausitz (Lusatian) mountains and the Erz (Ore) mountains. Saxon Switzerland is also a beautiful natural park on the Czech border.
Dresden is known to Americans mainly as "the place the Allies bombed the crap out of during WW2," but Dresden has a cultural history which earned it the nickname "Florence on the Elbe." Notable sights include the Frauenkirche, the Hofkirche, palaces, museums, and gardens.
Near Dresden is Meißen, known primarily for its porcelain industry. If you have 30,000 Euro to spend on a tea set, you'll be buying it from Meissen. It's beautiful porcelain, to be sure, but I don't have that sort of money.
The other city of note in Saxony is Leipzig. I took a day trip there from Berlin last year and wandered through the old city. Notable sights include the Thomaskirche, where Bach worked as cantor for a while, and city halls (old and new). The restaurant where Goethe ate as a student and is home to a scene from Faust, Auerbach's Keller, is in the basement of what's presently a shopping plaza. My friend and I didn't eat there, because it was too expensive, but the statues of Mephisto tempting Faust and Faust's friends holding him back are on the public level. Rubbing Faust's foot is considered good luck for students, so it's a very bright gold.
Next stop: Thüringen.