Outside the vacation apartment, in addition to the above lines, there are a variety of excursion options in many different variations:
A hike around the Hufeisen-lake, which is only 2 minutes away, is always recommended. The Goitsche (large Goiitsch-lake) is also only 20 minutes away, the Cospuderner-lake can be reached in 30 minutes.
There are a few smaller bathing lakes nearby, also with nudist area. You could also combine this with bike and motorcycle tours.
Try the city center of Leipzig. Leipzig is known for its debauched nightlife.