In two days, I would do the following:

1) a walking tour of the city - we used Rick Steves, but many guide books feature similar self-guided tours. Or you can pick up a free guided tour at Marienplatz. This will acquaint you with the cathedrals and other touristed sites, like the Viktualienmarkt.

2) a visit to Dachau. I did this with a tour, but (especially with a car) I'd recommend you do it on your own. The exhibits are much more meaningful to contemplate, I think, without a guide chattering at you. At least that was my experience.

3) The Residenz and Treasury, for enlightenment, followed by the Hofbrauhaus, for the experience. (The Munich City Museum was awfully good, too.)

Enjoy your visit.

Well, it all depends on your interests, of course.

Without knowing more, I would recommend beginning with a walking tour of Munich to give you a good overview of the city. There are many companies that offer such tours, so just do a Google search to find one you like. Afterwards, I would visit a museum that interests you. Any guidebook will have descriptions of these or do an internet search.

On your 2nd day, start out by going to Dachau. If you have a rental car, you can drive there or if you prefer to take public transportation, that can easily be done as well. A thorough visit will take at least half-a-day, so get an early start if you want to do further sightseeing later in the day.

I think the Alte Pinakothek (old masters) and Glyptothek (classical sculpture) are 2 of the best museums in the world. If you like art, don't miss them.

King Ludwig II's crypt is in Michaelskirche. The Baroque Asamkirche is interesting too. If you climb to the top of Peterskirche, you have a fantastic view of Munich (including the Frauenkirche), but it is 306 steps.

There is so much to see in Munich, I would spend your time there seeing things in Munich and save Dachau until you were on your way to your next location, if possible.

If Munich is at the very beginning or the very end of your trip the first thing I would do is DITCH that car. All the places mentioned can be reached very easily on public transportation including Dachau.

Ditto Dukey1. Try to plan your trip so that you can pick up the car as you leave Munich or drop it off as you arrive. Public transport in Munch is great. We've visited Munich several times, Two weeks ago we had a two-day transit pass and used it extensively on the bus and metro, easily getting everywhere we needed to go. I'd add a visit to the Viktualienmarkt (near the Marienplatz) as a must-see.

As others have said, "it depends on your interests" but two things to consider are ... the Deutsches Museum (a huge hands-on science museum). You can plan as much time as yiu can spare, you probably won't cover it all. The second thing is the cheesy but fun Bavarian Folk Evening at 7 pm each evening at the Hofbrau Haus.