A few relatively rare WW2 aircraft and other cool stuff).

Eat in Munich: Hofbrauhaus Munich (probably corny German beer hall experience dedicated to tourist but cool nonetheless, big communal bench tables, etc. [if you want to go full corny/American tourist there is a hard rock cafe across the street, it's as good as you think as in not very])

Nearish Salzburg: Koenigsee, Berchtesgaden (all associated Hitler sites: small documentation center, tunnels, foundation of his Schloss, the eagles nest), salt mine tour in Berchtesgaden is fun but probably better for families with kids rather than a couples event, Rossfeld panoramic toll road, Schloss Hellbrunn grounds tour

In Salzburg: Mozart's geburtshaus, walking around, free tours are fairly easy to find iirc.

Sounds like you are already doing Neuschwanstein. Near there is the Wieskirche, a baroque Catholic pilgrimage church that is in the middle of nowhere small but very impressive, worth a quick side visit if close by but don't dedicate hours to it.

Eat: in Salzburg St. Peter's stiftkulinarium. Supposedly oldest still operating restaurant in Europe. The courtyard is a nice place to eat, tradition southern German/Austrian fare.