The beer garden at the Chinesischer Turm (Chinese Tower/Pagoda) in the Englisher Garten is a particularly nice one to visit, I've found. There's also one in the Viktualien Markt right in the heart of the old city that can be especially nice for people watching.

In the city you can also visit Schloss Nymphenburg - a pretty & easily accessible palace and be sure to wander the grounds, as there are some neat hidden treasures (eg.the bath house that has an amazing tub - room-size, if I recall correctly). Schloss Schleissheim is another palace that is very near Munich, but in the suburbs a bit -- it is easily accessible via S-Bahn. These palaces are convenient, but Ludwig's castles that someone else mentioned really are the fairly obligatory ones. I would also add Herrenchiemsee to the earlier list - and it is off in the same direction from Munich as Neuschwanstein and Linderhof.

Have fun! Munich is one of my favorite cities and, as others have said, May is a great month.