Things to do in Munich

A few things would be - day trip to Fussen to see the Ludwig castles - day trip to Salzburg - visit Dachau concentration camp (if you think that would interest you) - the main square is great to walk through
- if you are into cars - the BMW museum Enjoy!

Honestly, one of my favorite experiences in Munich is just hanging out in a biergarten in nice weather, drinking beer, eating giant pretzels and enjoying the atmosphere. The English Garden is beautiful and well worth a stroll (the main biergarten there at the Chinese Tower is fun). Go to the Schwabing neighborhood, right by the English Garden, for strolling, people-watching and having a bite to eat. The Old Town area is pretty compact and easy to cover on foot. Start at Marienplatz (I wouldn't bother with the glockenspiel performance unless you just happen to be there when it begins) and just wander. Pop into the Frauenkirche and Peterskirche, both beautiful. Visit the Viktualienmarkt and browse the stalls. If you're into art museums, visit the Alte Pinakothek, Neue Pinakothek or Pinakothek der Moderne, depending on which ones are to your taste. If cars are your thing, visit the BMW Welt and museum or take a factory tour. The Residenz or Nymphenburg Palace are worth seeing (but I'd do one, not both). Whether to do a day trip depends on how much time you decide to spend in Munich. Dachau is close to the city, but with only 3 or 4 days I'm not sure I would go too far afield. If you really want to see Neuschwanstein/Hohenschwangau or another part of the Bavarian Alps, maybe you could stop over en route from Italy and stay one night before heading on to Munich. I didn't find Salzburg all that appealing, but I realize I'm in the minority.

Other suggestions: Lunch at the Hofbräuhaus, Deutsches Museum, Schloß Nymphenburg, Dachau, Münchner Stadtmuseum (exhibits in German but always interesting).

I would go on a walking tour or bike tour, to get a good orientation to the city and learn some of the history. Read up to date reviews for the best ones over on Trip Advisor. Without knowing your interests, it is difficult to make any other suggestions, as far as museums or other tourist attractions.

This begs the question... if you're flying into Munich, why go all the way to the Dolomites, which are just one small area of the much larger Italian Alps? The Tyrolian and Bavarian Alps are right on your doorstep from Munich. Munich is a very bicycle-friendly city. I would recommend renting while there. As others noted, the old center is fairly compact, but neither is it tiny. Cycling is a very effecient method of getting around the city. Another daytrip option would be Chiemsee.

Beware of Oktoberfest is you are travelling to Munich in late September. However, a pretty cool "one day" experience is as follows: Begin with the Frommer's walking tour #1, free on-line, which begins at the Frauenkirche and ends at the Konigsplatz. Take the subway from there to the main train station and pick up the Tram #17. Ride the Tram 17 to Nymphenburg Palace and tour. After touring, walk to the Hirschgarten, which is the largest beer garden in the world. Have a glass of the famous Augustiner Brau beer and watch the deer frolic. If you haven't eaten, they also have some pretty tasty food items. Catch the Tram 17 back to the main train station and if you are so inclined, stop by the Augustiner Keller, which is on the way!

In addition to the other suggestions, I really liked the zoo. It started to rain and we went into a cafeteria (inside the zoo). Munich is my favorite city, at least for now.

Karen: The suggestions you've received already are good about what to see. You might find rooms in Munich difficult to find from 18 Sept until the first weekend in October. Oktoberfest is really something to see if you can find rooms. The Dolomites really are not really served by train routes. Your best bet would be to rent a car when you leave Munich. Drive down to Zell-am-Zee, Austria and spend the night. Then enter the Grossglockner High Alpine Road, which goes over the Alps to Lientz, Austria. It's the second highest point in Europe with scenery beyond belief. There are really nice reasonably priced accommodations around Lientz, and the Dolomites are closeby. GoogleMaps and Mapquest cover all these areas. Leaving, you'd go west to the Motorway and north through the Brenner Pass into Innsbruck.
It's an easy trip back into Munich from Innsbruck.