I should have recommended the city where I was living for more than 3 years and a half, a long time ago because it is a city you get to love and that you miss when you are no longer in there. But never is too late, so here you are!
Some sightseeing tips:
The beautiful Mariemplatz with the Rathaus (city hall) and the Frauenkirche (Women´s cathedral)
Die Viktualienmarkt - > here you can find many stands where you buy fresh food or even have a meal in a Biergarten
Die Hoffbräuhaus -> A living Oktoberfest atmosphere throughout the year!
Maximiliemstrasse - >one of the most exclusive shopping streets in Munich
die Universität (LMU - Metro : U6) Hauptgebäude
Die Pinakotheken (alt und neu)
Olympiazentrum and the Olympic tower (if you dont have a vertigo)- the old Olympics city within Munich now turned into a student´s neighbourhood
and of course if the weather allows it , take a stroll around one of the biggest parks in Europe : der Englischen Garten and go in direction to " der Chinesische Turm" (The Chinesse Tower)where you can have a "Bier Mass" and a "Bratwürst" -> traditinal German beer from Bayern and sausage
You can also have a traditional picnic along the river "Isaar" in the summer (beautiful!)
Schwabing -> die Wiese (where the Oktoberfest takes place in late Sept-oct ->the biggest Beer Party in the world!)
if you are going to stay longer than 3 days , you can also go to the:
Nymphenburg Palace of barroquian style with its beautiful gardens.
and if you are a football fan , try to watch a match at the modern Stadium "allianz Arena"
Dont leave Munich without eating a : Brezzel, Wiener Schnitzel,white sausage with sweet moustard or Schweine Braten (if you are a Vegetarian then ,no chance!)
and of course order either a : Helles or a Weiss Bier!
In relation to transportation , Munich is a very well organized city, if you buy a day ticket you should be able to use the bus, underground and trams. Check the zones for the city centre unless you are going to see a lake or a palace that maybe outside the city. The only inconvenience is the machines for the tickets that are mostly displayed in German and can be a bit complicated to understand due to the multiple options so try to buy the tickets for your stay at the train station or Airport where they will speak in English to you.
Best time of the year to go to Bayern in general is either the spring or the summer, where you can have a swim in any of the gorgeous lakes around Bayern, like the Chiemsee or Stanbergersee! Unless you want to enjoy the Xmas markets on the streets with hot wine or if you want to go to the Oktoberfest (not my liking, though.., too crowded and expensive although i love the German guys in leather trousers!).