The closest ski area with plenty of green (I guess you mean blue, which means for beginners in Europe) runs I can recommend is Schruns/Hochjoch in Austria. Takes 4-5 hours by train, though.

http://www.montafon.at/Panorama-map-winter-313-en.html

I.

Ingo knows more about Europe than I ever will....but I have been to Garmisch..... and while not the best ski area, has pretty much what you would be looking for in a ski area close enough to Stuttgart.

-john

John, I also thought about suggesting Garmisch. But a) it doesn't exactly fit the 2-3-hour train ride criterion (granted, Schruns doesn't either) and b) there are not that many runs for beginners there - and those that are for beginners are not very snow reliable. Right now the snow situation is totally poor and it doesn't look like it will get any better soon. So I decided to recommend Schruns instead which clearly has the better options for beginners and is more snow reliable (not the village, but the runs).

you are highly unlikely to get what you are looking for within 2-3 hours of Stuttgart.

if you are prepared to think about places within 1-2 hours of Munich, the answer would be vey different - Seefeld, Mayrhofen, Saalsbach, Kitzbuel, Garmish...there are loads.

but you need to think about what sort of resort you need - beginner "green" runs are usually found at the foot of the mountains where ironically the worst snow may be, making skiing much harder. Go higher up, and you get better conditions but the number of green /blue runs may reduce.

an area you might like to look at is the Wildkaiser in Austria - there are a number of resorts of different types all grouped around the main resort of Sõll, all on the same ski pass, so you can "mix and match" according to the conditions and what you decide you want to do.

Thanks so much for the very informative responses! This will be very helpful in our planning!