"...Berchtesgaden and then continue to see some parts of Germany like Bavaria with traditional old Towns and Castles like Neuschwanstein."
Bavaria is a logical place to visit. It's a lot bigger than you may think, actually. Once in Berchtesgaden, you are already there. It extends north, nearly to Frankfurt - see map.
For well-preserved old towns, castles, etc., you should probably consult the UNESCO World Heritage list for Germany.
BAMBERG and REGENSBURG are probably the two best-preserved places of all (despite the skimpy coverage they get in Rick Steves' book, which tends to send readers to more touristy places.)
Neuschwanstein won't be on the UNESCO list. It was built just before the dawn of the 20th century, long, long after most castles had already crumbled, and is not a genuine castle, but a residential palace with a faux castle facade. It's notoriety among international tourists stems largely from its use by Walt Disney (who was born around the time N'stein was built) as a model for his Disney-park "castles.")
Some authentic castles can be found in the Salzburg area: https://www.salzburg-burgen.at/en/
Burghausen is near the German/Austrian border: https://www.visit-burghausen.com/en.html
The Bavaria Ticket is a day pass covers virtually all of Bavaria by train, bus, and inner-city transport (bus, tram, subway.) It doesn't cover transport within Salzburg but does cover transport from Salzburg into Germany. There are other handy day passes at even lower prices for smaller regions of Bavaria as well. All of the day passes cover regional trains (but not the super-fast long-distance IC, ICE, EC and RJ trains.)