Mhm, that's a rough one. It's not worth going to a small club imo. to get a real insight on what german soccer/football culture is about. You'd need to go to a top club.
The nearest "top" club is "KSC" in Karlsruhe. Next to Karlsruhe is "VfB Stuttgart" in Stuttgart.
I'd recommend Stuttgart, because they have a way bigger stadium, are on their way to the Bundesliga again and therefore have more fans in the stadium than KSC, who has a small "stadium" and is on their way to the 3rd League again.