Compared to other cities where I have dropped by briefly, I find it rather difficult to write about a city in which I have dwelt ten weeks--perhaps it is because after such a period of time, there is simply so much to write about, and so much nuance about this fascinating city that I cannot even put to words.
First Sight
If you arrive in Munich by plane from the north, as you descend beneath the cloud-sea in the daylight, you will see green fields speckled with red-roofed buildings--not yet Munich, but Bavaria.
Munich, like other major cities, is a conurbation with several satellite cities. Munich's sphere of influence fades gradually with distance, but roughly to the north along the Isar (a river that goes through Munich), the communities appear as follows.
To the left bank of Isar, there are Studentenstadt, Fröttmaning, Garching, Freising, and Moosburg. To the right bank of Isar, analogous to the respective communities are Oberföhring, Unterföhring, Ismaning, etc. Fröttmaning hosts the Allianz Arena, where some of the 2006 World Cup matches took place; Oberföhring is the community where I lived; Garching is roughly where I worked; and the airport (Flughafen) is close to Freising.
I do not know too many communities to the south or west, but one notable community to the north-west is Dachau, which houses the first Nazi concentration camp--a bleak, imposing, but lifeless series of constructions.
Isar is quite a large part of life in Munich. It originates from the alpine meltwater, passes through Munich, and goes into the Danube River further north. As a northern extension of the Englischer Garten, a rather large park / greenspace near central Munich, there is a linear greenspace along the Isar, all the way to Freising (some 30 kilometres out) and beyond. Paths along both sides of the river are suitable for bicycles. In fact, several times I commuted to work by cycling along such a path from Oberföhring to Garching, a trip of about 12 kilometres that can take up to an hour (ok, I suck at biking).
Centre
According to Dr. Georgii, the centre of a German city is marked by the Dom. But it is true that not every city has a Dom: only cities where an archbishop is available can have a Dom. Fortunately, there is an Archbishop of Munich, so the city centre is usually considered to be the Dom, and the pedestrian Marienplatz in front of it.
South of the Marienplatz lies the Viktualienmarkt, where a variety of food and other goods are sold. Restaurants surround the market. Nearby, the Peterskirche has a tower that offers a view of "München auf einen Blick" (Munich at a glance).
To the west of the Marienplatz is the Karlsplatz, marked as a circular square with a fountain. The stretch from Marienplatz to Karlsplatz is probably the golden section of Munich--filled with high-end shops and stores.
East of the Marienplatz is the Isartor, just before a bridge that crosses the Isar. Built on an island in the middle is the Deutsches Museum, reputedly hoarding many technical objects. Alas--during my stay I only had the chance to loiter near the entrance of the Museum but never had the time to go in.
To the north of the Marienplatz is the Residenz; with its Schatzkammer (treasury) and its palace, it could take hours to visit the place thoroughly. When I was there in the middle of June, I arrived about 45 minutes before the closing time, and had to race through the two halls. However, I stopped enough time to take a good look at the famous statuette of St. George.
Going further north, one hits the Ludwig-Maximilian-Universität (LMU). There seems to be some strange rivalry between the Technical University (TUM) and LMU, and my colleagues at the TUM often jokingly call LMU "Lower Munich University". That aside, the main hall of LMU is very majestic--way more than a typical Princeton hall. Towards the end of July, I had the opportunity to listen to Mendelssohn's Elias in the LMU, and I was impressed as much by the chorus and the orchestra combined as I was by the architecture of LMU.
North of the LMU is the Siegestor, likened to the Paris Arc de Triomphe. The LMU is also on the western skirts of the Englischer Garten. Though it is a "garden", it is in English style--so as opposed to well-tended and somewhat artificial French gardens, English gardens often appear much more wooded, wild, untrimmed, and natural. As mentioned above, the Englischer Garten is huddled against the Isar River, and its north extends some greenland all the way to Garching and Freising along the river. Englischer Garten also houses many surprises, including several reputedly quite good biergartens.
North of the Siegestor one enters the area of Schwabing, a rather expensive area where four-floored apartments are more common. This area resembles a commercial node, much like Oakridge in Vancouver or Gongguan in Taipei.
Transport
It's complicated! Buses roam the city, and I use it almost daily in my commuting. But for some procrastinating reason I always needed to run in order not to miss the bus (often comes in regular intervals of 10 or 20 minutes). There are also many tram lines in the city, bus-like vehicles that run on rails, but obey red lights (unlike the metros).
The U-Bahn, the underground train, resembles the metro in many cities, but the doors often will not open for you--the passenger needs to open the door him/herself. The U-Bahn usually has six cars, but the length is reduced in the night. Also, in the night, some U-Bahn lines and operations will change (i.e. some trains will only drive to an intermediate stop and no further). The first time I encountered this I was given a nasty surprise. Evidently not all people in Munich were familiar with this; I have seen two people who did not come out when the driver announced the end station, and were thereby stuck on the train.
The next level up is the S-Bahn, the suburban train. These trains run further into the satellite towns around Munich, but fares go up almost exponentially with distance. In the "central corridor" of Munich, the S-Bahn is the easiest way of getting around, since different lines come from different directions, but most of these lines converge ath the central corridor, so often there is an S-Bahn every 2 or 3 minutes along the central corridor (even though each line issues a train every 20 minutes or so). Munich is a monolithically large city, such that the S-Bahn is simply a larger version of U-Bahn. But in other areas where there are many cities nearby (i.e. Mannheim, Heidelberg, Karlsruhe), the S-Bahn is an easy and cheap way to get from one city to another, as well as intermediate stops.