Göttingen is not a touristic city. This is a typical "German" with all standard cliches: station, old city, Market Square, City Hall, a small river. Nothing is known in terms of tourism here.
The only thing that the city has to be known of is a university, where brothers Grimm taught and Heinrich Heine, Bismarсk and Dieter Bohlen studied. Symbol of the University, Goose Girl Lisa, now stands on the central square. By tradition, each student who receives their doctorate has to kiss Lisa.
Old city is available, but it doesn't look like a real old city. Beautiful buildings stand together with horrible ones. I cannot understand how it was possible to build Karstadt in the historic center.
To photographers I would suggest to go around the center, as nice pictures can be made in few places only.
Göttingen is good enough for weekend trips. However, there are many tourists and locals in the center, so come early in the morning or on weekdays. The city is also suitable as a base for further exploring the nearby regions.
Getting there: Göttingen is an important railway junction, so it's easy to get there.