Last year, I had the same problem like you guys.
If your son is turning three next month, he won´t be accepted to any of the "city"kindergardens. All kids that turn three after October 31 must wait till next year.
There is a great place (highly recommended) in Balanstraße. Day care is called Kinderhaus Laterne. It is a private place but I think they are not overpriced and they offer a great programm in german, english and french. You can also apply for the substidy by the Jugendamt and then you pay less. My kid was 1.5 years old and he went to day care there and the normal price is 561 (I think) but we had to pay only 203 €. It is worth appliing even if you earn a lot because they always give you something (they are aware of the situation with kindergardens in Munich) The place has great working hours (7:30 - 18:00) and they also offer weekend slep-overs once a month.
Here is the web-site
http://www.kinderhaus-laterne.de/
Here are the prices: Ganztags: € 412,- + € 41,- für Essen and you can get substidy up to € 373,24 by:
Stadtjugendamt München
Abteilung Wirtschaftliche Hilfen
Orleansplatz 11
81667 München
Tel.: (089) 233-259 37 (Vorzimmer)