The Gewandhaus also has tourist tours, which is helpful in the months when there is no concert activity. I found the tour helpful in understanding why Kurt Masur, while Music Director of the New York Philharmonic, was so relentless about how awful it was to have a concert hall with no pipe organ.
I think I forgot to mention the not-too-far Dessau-Wörlitz Gartenreich, a UNESCO World Heritage Site, and a great, mostly outdoors, sort-of "Executive" Open Air Museum. Even among the remains of Imperial Europe, it's an unusual place. There's a restaurant-road with many outdoor cafes nearby (walkable), don't know if it has a special name.