Google Maps gives a couple different routes with travel times within about a 40 minute range.
Based on you wanting to go to Neckarslum, I'd say the Dusseldorf - Frankfurt - Heidelburg - Neckarsulm - Augsburg - Munich- Salzburg route looks like the best option.

Although a more northerly route from Neckarsulm - Nuremberg - Regensburg - Passau - Salzburg would be nice too.
Regensburg would be a good place to spend a night. It's a nice town with enough to see and do or venture out to Kloster Weltenburg for a beer and dinner.