You can spend an entire day in and around Marienplatz. Start at 11 AM with a performance of the Glockenspiel (playing clock) at the Rathaus (city hall). If you get there early, you can walk the Fußganger (pedestrian) zone toward Karlstor. It's a great place for window shopping and people watching.
After the performance, look over your right shoulder. See the church tower behind you. That's St. Peter's. For a couple of Euro you can climb up the inside to the observation deck almost 300ft up. From there you get a marvelous view, on a clear day to the Alps, out across Munich, including the Olympic Park, and down into Marienplatz. Note the church to the left of the Rathaus, the one with the green domes on top of the unfinished spires. That's Frauenkirche, one of the symbols of Munich.
After the view from St. Peter's, go have lunch at the Ratskeller, in the basement of the Rathaus. Weißwurst (white sausage) is a traditional meal of Munich.
Tour the Frauenkirche or the Viktualienmarkt, or walk down Talstrasse to Isartor, one of the original gates of the city wall.
For the rest of the afternoon, you can tour the Residenz. I found the Residenz interesting at first, but it quickly got tedious, with it's seemingly endless progression of too-gaudy Rococo rooms.
Another possibility is the Deutsches Museum. However, it is extensive. I wouldn't even venture into it without a couple of weeks to devote.
My favorite place is the City Museum of Munich, a few blocks south of Marienplatz. The last time I was there they had an exhibit of Munich as it developed through the years, with drawings, maps, and models. The museum is entirely in German, but dates are pretty universal.
You could finish your day with dinner at the Hofbräuhaus. The food is inexpensive, the beer is great, and the entertainment, although corny, is traditional and fun.