Neuschwanstein Castle, Linderhof Palace, Berchtesgaden, and the Eagle's Nest are lousy day trips from Munich, but they are right next to Mittenwald where you plan to spend a night. But you can't do them all in a single day. If the weather's good the Eagles Nest is also; the views can be spectacular. Linderhof is one of the best Schloss' type castles, period. It's magnificent. Neuschwanstein is very touristy; right up there with Rothenberg odT (RodT)or Octoberfest as a symbol of having been to Germany. If you can book a tour with Neuschwanstein, Linderhof, Hohenschwangau, and Oberamergau (they do exist) that will be a very full day.
Nuremberg is an easy train ride to and from Munich. You can walk right out of the train station and across the square and into the old town. I lived between there and RodT and even wrote up a basic inside the walls itinerary for a days walking tour. But it's such a fantastic place you do yourself a dis-service trying to do it all in one day. Here's a short list of stuff to do there:
The Train Museum
The Toy Museum
The Kunst Quarter
The Stadtpark
Westfriedhof - Cemetary
Johannis Friedhof – Tomb of Albrect Durer
The Cupernicus Planetarium
Trodelmarkt
Tucherschloss
The Tiergarten
Kristall Palm Beach (not really in your focus, but a lot of fun...)
The Water Gate
Imperial Castle & Gardens
National Germanic Museum
City Walls
Lorenzkirche
Hauptmarkt
Beautiful Fountain (Schonnebrunnen)
Gansemannchen Fountain
St. Giles Church Frauenkirche
Albert Durer House
City Museum (Fembo House)
Tiergarten Tor - Medieval Square Frauntorturn District - half timbered houses
Weibergasse Street
Weinstadel House
Zum Guldenen Stern
Nassauer House
Tugenbrunnen Fountain
Museum Bridge
St Sebaldus Kirche
You might also want to check the calendar for the Messecentrum and see if they have a show going on while you are planning on being there. First, because that affects hotel availability and pricing, and second in case it's something you're interested in.
I won't bother with a list for RodT, because that gets written up by every tour book author. The thing is you could easy spend a week within 50km of there and not see everything. (Castles, meteor craters, dinosaur beds, etc.)
But here's the thing, you cannot possibly see Munich in 3-4 days. Not even just the "old" part of town.
Dachau is a day. Yes, the tour doesn't take more than 3-4 hours, but I've taken several groups of friends thru there and afterwards nobody wants to do much except maybe sit and drink. It's a graphic display of just how terrible people can be and emotionally draining.
If you tried to do three museums a day it would take more than a week to do those within the city limits. Churches would be about the same. Shopping, beerhalls, architecture, historical sights; there's just so much. And then there's music, street performers, the State Opera, and special events that take time too.
I've written pages of notes on these places for friends going over. Nobody ever has enough time, myself included. Last time I flew into Munich I spent three weeks just driving around Bavaria, Tyrol, and the Czech Republic (all of which I know well) and I have a list of stuff I missed and need to go back for.