There is a pedestrian mall ('''Fussgaengerzone''' or '''Kaufinger Strasse''') that stretches from '''Karlsplatz''' on the western end to the '''Isartor''' on the eastern end. In between, you'll find great shops, touristy restaurants, the famous Munich church with it's two towers ('''Frauenkirche''') - which offers great views across Munich, and '''city hall''' at the '''Marienplatz''' with is famous Glockenspiel. As you stroll along, watch out for the "Zum Augustiner" (across from the "Dom - St. Michaels Church"), which is a bit more an original Munich beer hall, and not as touristy as the "Hofbraeuhaus".
As you make your way in eastern direction past the Marienplatz, turn to the right and check out the '''Viktualienmarkt''', a market place for food and drink that's been around (and is still in operation) for a few hundred years. Try some of the different foods on offer, and get yourself a beer from Munich. It's a place to look around and watch all the activity going on (as long as the weather is nice).
While we're at food, if you go back to the Marienplatz, and pass city hall on the right, after a block or so you'll wind up at Dallmayr (it's on your right). One of the oldest delicacy stores in Munich, go in and check out what they got (very pricey, tho), it's worth it. If you keep walking in the same direction, you'll wind up at the '''Feldherrenhalle''' on the "Odeonsplatz" (Odeons square). Around this area, you'll see some of the bombastic buildings of the "Wittelsbacher", the dynasty that ruled Munich for some time. There is the '''Munich Residenz'', the '''national theater''', the '''Hofgarten''' and the '''bavarian chancellery'''. (Right behind is the american consulate, that's where I got my first ever Visa for the US).