Can vouch for Berlin, too. In Berlin Mitte near Alexanderplatz there are great apartments for approx. $2k/month (around 60m2). It's one of the more expensive areas, but I think it's better for young families who want a calm place.
You will make way less money, though. $5-7k/month should be possible. At SAP you can make $10k/month after some years. But in general it isn't really comparable to US salaries.
For the lang. barrier: Most people speak english and there are many coffee shops where 80% of the employees can only speak english.
Alternatively: I heard that Zurich also pays good, but that the people are not too social and it can be hard to build a social circle there.