Badeparadies Eiswiese
One of Göttingen's public swimming pools, Badeparadies Eiswiese (http://www.badeparadies.d...), is a roughly 20-minute walk south of the city or a ten minute bus ride on line 4 or 14. But if you enjoy the water, they offer a plethora of swimming pools indoor, outdoor, large, small, hot, cold, saunas, jacuzzis, and solaria.
The Göttingen forest follow Herzberger Landstr. east is full of pleasant hiking trails, as well as the Bismarck Tower, which you can climb for a gorgeous view in the summer though you may need to ask directions, since the tower is hard to find.
Check the city calendar (http://kalender.goettinge...) for local events, or pick up a schedule in the Tourist Office in the old town hall. The symphony orchestra is impressive for such a small town.