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Numbeo.com has a lot of (crowd-sourced) information about local living costs.
In Germany, most costs except rent are very similar in most places.

Rent in Heidelberg is about 1500-2000 for a 2-bedroom apartment. I don't know about Leon St Rot, but I expect it would be less. Heidelberg is lovely but definitely on the more expensive end when it comes to rent. Best to check  immobilienscout24.de/
Just remember to include the nebenkosten in your calculations, and that Germans count apartments by number of rooms, not number of bedrooms (ie a 2-zimmer is a 1 bedroom, a 3-zimmer is probably a 2 bedroom, but check the descriptions carefully!).

Best of luck.

Heidelberg and its surroundings is a relatively expensive area compared to the rest of Germany. If you want to save on accommodation (which is the main expense of Heidelberg over surrounding towns and villages) then is best to live a bit out of town. Heidelberg itself, reckon on around €12 per square metre without bills & utilities.

Mannheim would be a viable alternative, in that it is a large city with plenty going on. It's a pretty ugly, industrial city though and nowhere near as nice as Heidelberg. Mannheim would be €9-10 per square metre as a comparison.

gives you the lowdown on general expenses in Germany to give a good idea.