Can anyone recommend a jazz club in Munich or Rothenburg?
No, but I can recommend a couple of Jazz Festivals that will be taking place soon in the Rhine Main Region. 8-10 June, Jazz Fest in Bad Homburg 15-17 June, Jazz Fest in Idstein
http://www.idstein-jazzfestival.de/ Jazz in the Frankfurt Palmengarten is another old tradition, dating back to right after the war ended. Frankfurt was a hotbed for Jazz enthusiasts. Website is in German, but dates are there as well as artists. http://www.jazz-frankfurt.de/?cat=7 Sorry I couldn't help more with Munich and Rothenburg.