We have narrowed down our search to Fairfax County so considering the McClean and Fairfax areas as well. It's hard choosing where to live in an area far from home when you don't know anyone to tell you the neighborhoods that you want to avoid or seek out!
If you want to message me, I'd be happy to make neighborhood suggestions. However, I would not even attempt to do so without knowing more information about you all. Ages of kids, activities you want to be near (competitive sports, outdoorsy activities, culture, drama, etc.), are you looking for an HGTV home, or an older one with character, how much can you pay? How much are you willing to fix up? And the absolutely most important one: where is the commute. Even different parts of DC make a big difference. Do you realize the price of commuting? Is there a subsidy, or free parking? I've lived in a number of areas of Fairfax.
One thing to keep in mind is that 'affordable' housing (under $500k) is in pretty short supply. Are you wanting a single family home, townhouse, condo? I could make some suggestions right now but they may not fit your families temperament. McLean has one personality type, Oakton has a different one, and Fairfax or Robinson are different still. Some are more diverse (demographically and economically) than others.
Anyway, without more details, and of us who live here really can't help a lot. There are a few places that you want to avoid, but not that many. Generally, the cost of the housing will indicate to you where those places are.