I lived in Berlin for a year and also spent a month in Dresden. I enjoyed Meissen, Bautzen (which no one mentioned), and the hiking mentioned above. Germans LOVE to hike and you can drink a beer at a cafe way up in the mountains. You can also do some wine tasting in Saxony but I don’t remember the name of where we went.

OP here. Thanks all for the suggestions. I've been to Prague and love it! But I'm trying to keep it as close to 3 hrs each way as possible. Thank you to the PP who listed the Swiss Saxony National Park. That is perfect for what I'm looking for!

I will look at a couple of the other suggestions too. Thanks all!

Dresden is great.

Potsdam is a very cute town and you could spend the entire day in Sansoucci visiting all the palaces and charming follies. It's also a very short train ride to Potsdam.