In principle, it is possible to get with [this request][1] all city boundaries in bavaria.
In detail, there are two things to consider: First, it also returns cities that have a common boundary with bavaria, although they are actually outside bavaria. This is a side effect of the query semantics I have not thought about: Ways are considered inside an area if they are completely on the border (which makes sense), and relations are considered inside if one or more of its elements are inside (which also makes sense on its own), but both together is a little bit odd.
Second, there is no connection between the place nodes and the boundary relations. In some cases, they may be contained as members in the boundary relations, but not always.
edit:
A, Ahh, now I understand your question better. [This query][2] finds all place nodes (I added those of type town to cover more places) and for each the area it belongs to. To simplify testing, I have restricted these again to "A..". Feel free to remove that condition, but the query then runs for several minutes.
You can in principle deduce the relation ids from the area ids: just substract 3.6 billion. However, if you want to query for postcodes and so on afterwards, it is likely that you anyway still need the area and not the relation. I've written about the issue in [this forum thread][3].
[1]: http://overpass-turbo.eu/?Q=area(3602145268)%3B%0Arel%0A%20%20%5Badmin_level~%226%7C7%7C8%22%5D%0A%20%20(area)%3B%0Aout%20ids%3B%0A&C=50.84858;7.10726;16
[2]: http://overpass-turbo.eu/?Q=%5Btimeout%3A900%5D%3B%0Aarea%5Bname%3D%22Bayern%22%5D%3B%0Anode(area)%5Bplace~%22%5E(town%7Ccity)%24%22%5D%5Bname~%22%5EA%22%5D%3B%0Aforeach(%0A%20%20out%3B%0A%20%20is_in%3B%0A%20%20area._%5Badmin_level~%226%7C8%22%5D%5B%22de%3Aplace%22!%3D%22county%22%5D%3B%0A%20%20out%3B%0A)%3B%0A&C=48.77067;11.02478;8
[3]: http://forum.openstreetmap.org/viewtopic.php?id=20090