Hello,
it kind of depends what you are looking for.
Personally, I wouldn't really recommend Schwabing (too many cheap pubs, but expensive nevertheless cos everyone wants to live there. I don't understand why - It's great if you're a student going on the piss, but otherwise... ). The Schwabing part of the
English Garden isn't so nice either.
Bogenhausen would not be my cup of tea either (too snobby).
Lehel is nice (nice old buildings, nice corner cafés), but it is expensive, and because it is central, you would be hard pushed to find accommodation with a garden.
Also nice, but a bit expensive is Nymphenburg, would be worth it though as you would be close to Nymphenburg Palace which has lovely large grounds for walks, etc. Lots of nice cafés too.
If you want a lively part of town but still nice, and central too, (nice restaurants & bars, huge central library, concert halls, headquarters for Munich evening classes, large indoor swimming pool ...), then my no. 1 recommendation would be
Haidhausen. Again, you probably would have difficulties finding a garden though.
Finally, if you would prefer something outside the city (=good chance of finding a house&garden), Holzkirchen seems to have a small but lively "English colony", I know some of the ladies there, they are really sound.
Good luck either way! And definitely try to learn at least some German as one of the posters suggested - generally you can do without, but it makes life a hell of a lot easier if you can speak the lingo. The Munich evening classes organization ("MVHS") also offer intensive German courses during the day, so this is definitely something worth considering when you arrive.