Halle is well placed for short excursions. Leipzig is 25 minutes by S-Bahn — easy to do as a half-day. Naumburg, with its remarkable 13th-century cathedral and the sculpted figures of Uta and Ekkehard, is under an hour by train. Eisleben, where Martin Luther was born and died, is just half an hour west.
For something quieter, the village of Goseck has the reconstructed Neolithic solar observatory — a circle of wooden posts on a hilltop — which pairs naturally with the Nebra Sky Disc at the State Museum of Prehistory.