Sorry TAP, the Hofbrauhaus is not in Marianplatz...it's about 4 blocks away. I know because I have been to Munich AT LEAST 100 times...and I have always gone to the Hofbrauhaus whenever I went to Munich...
...(I lived 40 miles from Munich for 4 years).
The castle at the bottom of the hill from Neuschwanstein is the Hohenschwangau.
Prague from Munich is doable in one day, but not a return n the same day.
Ceske Budejovice (Budweis in German) is a great town with a large square in the center. I spent several weekends there. The first time in 1991 when it cost $.26 for a half liter of beer up to 2004 when it cost about $.53.
The beer is excellent and definitely nothing like the American self-proclaimed King of Beers. Gottse dank!!! (Thank God).
True enough, passport stamps are a thing of the past in EU countries. You can still get them for places like Ireland, Poland, Czech Rep, Turkey, etc.
Telling you the best thing to do or see in one day is not really being fair to yourself if you are also trying to throw in Prague (northeast of Munich) and the castles (even further southwest from Munich)...I would concentrate on the Hofbrauhaus, the fest, the glockenspiel show at 11 in Marionplatz, and the fest...( I know I said the fest twice...
)...I'd recommend you add 2 more days to really see the sites of Munich.
If you're going to Prague...add another 3 days. One for Plzn, one for Prague and one for CB...
Overall, just have fun!!