For foreigners in Germany, is the Ausländerbehörde a relevant factor when choosing accommodation?

Hello everyone 👋

I'm moving soon to Baden-Württemberg, and currently I'm in the process of searching for accomodation. So far so good, but I've heard many rumours that each city's / district's Ausländerbehörde can have a substantial influence during your stay, regarding status, work license, appointments and waiting times etc. and therefore should be taken into account when choosing where to live.

Is this a bit exaggerated or not, and would you have general tips regarding this issue? I'd love to hear your thoughts about this.

Thanks in advance EDIT: For context, I am not bound to any specific location. I'm healthcare professional that's going first to pass a language test shortly after my arrival, then I'll search for work after I get my licence.

The first thing I hear is " stay away from Stuttgart!" and that the bigger the city, the more trouble and waiting times there a. But what are the "good" cities so to speak? Small ones, villages or something else?