For $1.2M, I don't think you're being unrealistic. I think the problem is that inventory is at historic lows right now, so you're just not seeing anything. I think you'll have more options after the holidays, leading up to spring.
I agree with a PP - your best bet is the neighborhoods close to East Falls church metro - Garden Commons, Berkshire Overlee, etc. We have friends with houses on Tuckahoe and Pocomoke in your price range. (the one has a smaller yard, though, but both houses are renovated and awesome.) You could also look a bit closer to Ballston, but as you approach Ballston, more of the homes will feed into Washington-Lee. Maybe something off of Sycamore? the closer in you are, the less likely you are to get a yard that's more than 0.25 acres, I think. Westover/Larchmont might work - it's around 1.5 miles from Ballston.
Also, it's great to be near Lee Hwy, just not TOO near. We live about 4-5 blocks from Lee and it's incredibly convenient. We're in Country Club, where your money could buy quite a bit, though you'd be a bit farther from Metro. We drive to Ballston and park at the mall when we want to metro in, or we can take a bus if I don't want to have my car. There are several buslines that go to Ballston/Clarendon/Rosslyn.
this doesn't have a huge lot but it fits the bill otherwise:
http://franklymls.com/AR7828838
this one has real potential (great neighborhood) and the updates wouldn't cost a ton:
http://franklymls.com/AR7925642
this is nice:
http://franklymls.com/AR7961761