I agree with rlchurch - if you live close enough to a metro stop, you won't really need a car, and when you need to go to IKEA (which is about 20 miles outside of the city), you can get a zipcar or flexcar for the day.
I have family living in Shanghai and taxis are very common and cheap. DC cabs are not cheap, and they can be hard to find if you're in suburban areas. I would take a look at a metro map here:
Metro - Rail - Maps - Rail/Google Map and then pick an area that is close to the metro, either by bus / walking.
I'm a fan of Northern VA and most anything on the Orange / Blue / Yellow metro lines that crosses through VA. Northern VA schools are pretty decent (compared to DC schools, unless you go private).
I would really advise against living way out in Herdon without a car. You need a car to get around in the more suburban areas of DC, otherwise you'll go crazy waiting on the bus systems. If you don't know how to drive, then that's another situation entirely, although there are lots of driver's ed courses in NOVA with all of the folks moving in from other areas.
Best of luck