By train, Weimar is only a quarter of an hour away.
Jena is just half an hour by train.
Leipzig is about an hour away.
Wander around on near-by Thuringen Forest, on which Thuringia called the "green heart of Germany".
Halle about 45 minutes away and has some great things to see. The largest city in Saxony-Anhalt is the birthplace of Handel and has a few castles.