Outside of Rome is a lot cheaper than central Rome, but you have to go quite a way before you get affordable places with gardens etc. (Though I suppose that these things are relative.)
North / north east of Rome you could try Tivoli (about an hour by train as I remember) or Monterotondo - an increasingly popular place for young couples and families and a bit closer in.
South of Rome you have the castelli romani - a nice area with some lovely towns such as Frascati. Quite expensive though.
North and north east you have the coast, and can still find some decently priced places. In particular, Santa Marinella is nice, but count on an hour's train ride - and limited trains in winter and at night.
I know of some people that live pretty much in Umbria - around the Orvieto / Bolsena lake area (sp?). Up near Viterbo (if you're as vague as I am regarding geography) you get a lot of "bang for your buck" but you are some distance from Rome. I personally wouldn't commute that far ever day.
Hope it works out for you!
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