Don't discount FHs, especially for engineering. With the right niche you can out-earn almost every other graduate - say in chemical engineering, in some EE niches or with economics degrees that focus on a particular industry.

Also, rents in Jena, Tübingen or Ilmenau are often on a Munich level, but you can always find a few shortcuts (like living in Weimar and taking the train to Jena).

Lastly, if the bachelor isn't meant to be your final degree it doesn't matter as much where you got it.