What to do/see:
Museum
If you are into museum, I would visit the Alte Pinakothek (old paintings) or the Neue Pinakothek (modern art) or give the new BMW Museum (near the Olympiastadion) a try, where you could also visit the Olympia area, worth a a walk.
Something for the lady:
Kaufingerstrasse or Maximilianstrasse are the main shopping areas right in the City centre.
Sightseeing:
In town centre the Liebfrauenkirche, Marienplatz and absolutely worth a visit the Viktualienmarkt (market with beerstalls) are all at the same road and within walking distance. A bit outside the town there is the Schloß Nymphenburg with a nice parc.
Citycentre is worth to stroll around, many small roads with independent shops and bars/restaurants.
For a beer:
For a night out Schwabing is the area.
To advice some Beerkellers into town: Augustinerkeller and Paulaners are at the Liebfrauenkirche and the touristic hotspot Hofbräuhaus is on the other side of the townhall (Platzl 7) in a smaller sidestreet. Also many beergardens in every part of town.
Munich is the town where you´ll get your beer in bigger portions. Ein “Halber” is half a liter, a “Maß” is a liter of beer. Ein “Helles” is a lager beer, a “Weizen” is a wheat beer, with some lemonade in it it´s a “Russn”.
Best Local beers are Augustiner, Paulaner, Hacker-Pschorr and Hofbräu. I prefer Weizen, but give the Augustiner a try, lovely!
The Beerfest “Oktoberfest” is at Theresienwiese, about 2-3 km behind the mainstation. Beware, you won´t get into a beertent without a reservation, the prices (Maß around 9€) are expensive, many pocket thieves and they close down at 23.00.
To eat:
Bavarian food is something special.....
Local product worth a try is "Obatzer" a cheese cream made out of camembert with onions on fresh bread, a "Weißwurscht", a cooked sausage, eaten with your hands by sucking it with sweet mustard. Or try "Schweinebraten mit Knödeln" a porc dish with potato (don´t know the right word) mixedballs.....
To get to/from the ground
Take the U6 at Marienplatz (Townhall/ 5-600m from main station) direction Garching/Hochbrück, get off the train where all the red/white fitted People get off or at Fröttmaning, then a 10 min walk. Away section is to the right.
The fare is NOT included in the matchday ticket. A day trip ticket for around 10€ might be the best option.
Munich is the law+order capital in Germany. Bavarian police is famous for nick you fir no reason and fees for example for a piss in public are expensive and they control everything….. So my advice, be gentle, do what they tell you and buy tickets for the tube.