Back when I was in 6'th grade the school library had The Effects of Nuclear Weapons on the shelf and a couple of us read it. I know that doesn't match the current reading level rules, but we were too ignorant to know that the best authorities are sure we couldn't possibly have understand it, so we studied it anyway. If it had been part of the curriculum that might have been another story... It was fascinating reading. Nobody we knew had fallout shelters--nobody was going to bother nuking Liberia, and it wasn't in fashion back in the States.
People are still thinking about these things--more so as more and more countries decline to trust their erstwhile allies. (There's been a rumor for decades that Japan has all-but-final-assembly parts in hand, and if I were running Japan I'd have looked at Obama and completed the assembly.) Some are going to come loose, and some will be deniably shared with loyal partners.
So, what should you do?
Homeland Security thought about the most likely target (DC) and most likely weapon (small), and came up with some common sense suggestions. (Livermore helped) Don't run; hide for a day until the fallout dies away. The blast damage from a small bomb isn't gigantic. If you survive that OK, and your house doesn't catch fire, the biggest threat is the fallout--most of which decays to harmlessness in a few days. One day is what they suggest. One hour minimum sheltering where you are, and then getting into a place with thicker walls if it is really close by.
A car breathes (or else you'd suffocate on a long trip), so it will suck radioactive dust into the cab as you drive to escape. Plus, the car walls are kind of thin, and don't offer as much shielding as you'd like. And sitting in the worst traffic jam in DC history while radioactive rain goes pitter-pat on the windshield is probably not good for your blood pressure.
I'm not used to reading radiation safety discussions with doses this high--if your dosimeter shows 10mrad exposure people start asking questions about where you were and what you were doing. 10rad...
FWIW, chemical weapon defense is not too dissimilar. Hunker down someplace sheltered while things dissipate and don't run.