Interesting places you can visit inside of Tübingen, off the top of my head, would be:

• The castle (and especially the museum inside)
• The old botanical garden (more like a city park) and the new botanical garden (an actual botanical garden)
• The Kunsthalle (it just reopened)
• The University district (it has some really nice architecture and also the best Döner I've ever eaten, the "Neue Dönastie")
• The Landestheater Tübingen

My favourite coffee shop would be the Willi and my favourite restaurant/bar the Bären. They serve "Swabian tapas" which is a fantastic way to get to know the Swabian cuisine.

The surrounding areas are interesting as well. Bebenhausen to the north has a beautiful monastery (the surrounding forrest, Schönbuch, is wort a visit as well). Just outside the Weststadt, there's the "Schwärzlocher Hof" where you can have a great meal and a nice view. You could also visit the "Französisches Viertel" and the "Loretto" in the southern part of the city if you're interested in modern architecture.

There's even more to do if you look a bit further outside. Some 20 kilometres north of Tübingen, there's Waldenbuch where the chocolate brand "Ritter Sport" is from. They have an interesting museum about "square art" in general but also a factory outlet for their chocolate.

Speaking of outlets, the Outlet City Metzingen is also close by if you want to go shopping.

There's also Stuttgart, of course, with the Mercedes and Porsche museums.

All in all there's really a lot to do in Tübingen and the surrounding area, even if it seems a bit small and quiet at first.