Here is some information re apartments in Munich. I have no personal experience with them as I have always stayed for only a few days and most apartment rentals are usually 5-7 days or more. You could also try Booking.com as they have some apartments to rent-
airbnb.com (highly recommended)
This is a testimonial for the last listing from another website-
In May 2011, a party of 5 adults stayed in the apartment called D'Alex New York. There were 2 bedrooms with doors and one person slept on the sofa in the living room. The apartment was very clean, in a nice neighborhood, a 5 minute walk to the U-bahn station, and there was a very good restaurant literally right across the street. The apartment was well-equipped, including a laundry machine, and ran us (including the cleaning fee) jut over 100 Euro a night. I found the company owner, Alex, to be very easy to deal with and quite prompt to reply to inquiries.
We appreciated being in a residential neighborhood without a lot of tourist commotion, but it may not be what you are looking for. I didn't have an opportunity to look at any of the owner's other properties. Once you're on the main page of his website, if you scroll to the bottom & click the Apartments link, it will show you all the choices.
Hope you have a great stay in Munich!!!