My advice - if you only have two days in Munich, stay there. There is plenty to see for two days; you won't run out of things. If you try to go out of town, you will just spend more time traveling and see less.
Oh, if by the N Castle you mean Neuschwanstein, it is not to the north of either Munich or the Eagles' Nest. It is almost due west of Eagles' Nest and south-west of Munich.
The only thing commonly seen in Munich that is not in the inner transit zone is Dachau. If you don't want to see Dachau, you can get to everything else with an inner zone MVV Partner Tageskarte (day ticket) for €9. That pass gives up to five people unlimited use of the S- and U-bahn, streetcars, and buses in the inner zone for a day.