During the last week of February I'm spending 3.5 days in Munich before heading to Salzburg. I'm planning to hit Marienplatz, St. Peter's Church, Viktualienmarkt, Hofbräuhaus, Frauenkirche, Dachau, and maybe the Residenz in the first 2.5 (I like to get out early and move pretty quickly). So my question is, what to do with the extra day?
I'm not a beer person, and I like historical sights, museums, and cultural experiences. Would I be better off exploring Munich more (other can't miss sights?) or doing something like Nuremburg for a day trip? Obviously it might be on the cold side, so indoor sights are probably preferable to outdoor ones, all other things being equal.
I've already decided to skip the Ludwig castles and save those for another trip when I can rent a car, as they seem like a bit of a hassle to get to via public transport.