I can offer a mix of first- and second-hand info. Please check it before you rely on it.
I think EDDM doesn't allow VFR < 2000 kg. IFR is allowed with PPR, which I've never tried to get.
EDMO doesn't take private flights.
A colleague used Augsburg (EDMA) as an IFR airport for Munich. Public transport from Augsburg into Munich is easy, almost as easy as from EDDM.
I've used Ingolstadt (ETSI) which is a little further north. Easy and accommodating, but not as easy to get into Munich. [Edited to add, actually, the train time looks like 40 mins just like Augsburg, and it was relatively easy to get to the station.]
For VFR, Fürstenfeldbruck (ETSF) and Oberschleissheim (EDNX) are possibilities with reasonable runways, there are other smaller fields around if you can get in and out. EDNX has a limit on the number of annual movements and requires PPR.
I find
eddh.de - Landeinformationen useful for planning destinations and stops in Germany.