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Munich is surrounded by nice places fitting your description.
However, as you have already noticed, you need to go quite far from the city: Rosenheim and Starnberg are over an hour drive from Munich and, since most people commute to the city in the morning and back out in the afternoon, expect frequent jams and delays.
The public transport network is very good and brings you back and forth easier and faster.
Also, you can't save much in living costs and rent by moving further away, since it's mostly the rich who do that.

Beppi, thank you. Any suggestions for places outside of the city like this?

If money is no issue, I would chose Starnberg.
You'd rub noses with politicians, industrialists, actors and other VIPs.

I used to drive to Munich once in a while from the Stuttgart area. Always went in the night. Was then able to get from the outskirts of the city to the center in 15 minutes or so. Driving others times like mornings and late afternoons聽 the same route would always take at least聽 an hour of bumper to bumper traffic. Thus having an S-Bahn connection to get a ways out of the city is a huge plus.

But of course the places well connected to such public transportation are going to be in high demand. If one already has a car then it can be a good strategy to combine it with trains. Thus you find a quiet village or fairly rural place where you might have to drive some kilometers to reach an S-Bahn. Sounds redundant to have a car yet regularly use public transportation but this gives you flexibility and eliminates the rush hour drives. If you would be close enough you might even get to the S-Bahn by bike.

Around most major Germany city are park and ride schemes there are designated S-Bahn stations to encourage such a strategy. One gets a discounted price for parking right at the station and the ticket into town.聽 The communities support this to try and lessen the amount of commuter traffic. But while I hugely appreciate the extent of public transportation in Germany, it is not exactly cheap. Thus if one is regularly commuting then it really makes sense to buy at least monthly if not yearly passes.

It鈥檚 not the same situation but I thought I would mention that I actually sold my car this year. City driving, parking, repairs etc. for a car I only used sporadically and the fact that I already did most trips by foot, bicycle or public transportation made me realize I could live better without a car. I joined the Stadt Mobile car sharing plan which exist in Munich as well and there are additional such schemes for people who occasionally need a car but don鈥檛 want to own one.

Unfortunately, I cannot say where the best area is for you to look for forest. Stuttgart has a lot of it not just on the outskirts but snaking into parts of the town. But this is because of its hilly terrain. Munich and outskirts are simply flat and mostly plowed under. Yeah, one has the beautiful Alps in the region but they are farther than some people might think and well beyond a commuting distance.