Good suburb to live in and around Tübingen

Tübingen is a university town and very liberal and open to foreigners. One doesn't need to know a particular area, it is all around. The problem for many is that it is expensive for accommodation. For people with a car sometimes living in a small community say 20 KM away might be cheaper. But these are more likely the kind of places where the people are conservative and not as open. So best to stay reasonably close to town. Reutlingen is a prosperous city nearby. Not as liberal as Tübingen but not a problem in any way.

Not sure what you are looking for in schools. The normal public schools are excellent. Private schools cost a fortune and aren't usually any better from an academic perspective. As an alternative, there is a Waldorf school in Tübingen; private but they charge according to one's income.