Munich is a great city to bike around. When I visited a couple years ago I remember seeing places to rent bikes around Marienplatz, including the train station. A lot of the city is within walking distance, but with a bike, you can easily get out to the biergarden, if you like parks within cities.
We didn't do much research before going to Munich, so we took a bike tour with Mike's Bike Tours, http://www.mikesbiketours.com/1.html. We had a good time, although we went in the off-season (Oct). I hear in the summer the tour can get a bit college partyish, depending on who is on the tour.
If you are in Munich for multiple days, I also recommend you visit Neuchwanstein Castle. In addition to the castle, there is a gorge to walk through, and other hiking trails if you have time. It is a good day trip, and can get there easily by train.