What a messy area for "private" flying.
To put this a little bit into perspective: Downtown Munich is to Germany what Manhattan is to the United States. More or less. It is the most sought-after location to live and work, offers the best paid jobs and also has the highest prices for land and rent in Germany. It is close to mountains and lakes, cultural and historic sites and has the Oktoberfest, therefore it is in high demand with tourists as well.
How close to Manhattan can you fly with a small private plane? How long will it take with public transport to reach the town centre from there? I have landed in Teterboro once and can tell you, that you will reach Munich centre quicker from every airfield named in the posts above than Manhattan from Teterboro...
But you are right in so far as small airfields are not usually served well by public transport in Germany. Anywhere, not just Munich. Even if they let you land at Munich airport you need a taxi to get from the General Aviation Terminal to the Airline Terminals where the train station is.
The best would probably be long-term car rental (or actually buying a cheap car and selling it on after your stay) and pick one of the general aviation fields around Munich which suits your needs best (runway, VFR/IFR, night, hangar, ...). There is quite some choice within a 45 minute drive from downtown Munich. (The train from the large airport to the centre takes 25 minutes, so you won't be there any faster anyway!).
Regards
Max (from Munich originally...)