It's been warm this year. Peak leaf color in Shenandoah is probably a good three weeks away.

I agree with the previous posters that a car is going to be a hindrance more than a help. If you have some locations you want to visit that require a car (like Shenandoah and, I guess, eateries in Arlington), why not a one-day rental? Any day you're spending in DC is a day you're going to be paying for your car to do nothing but sit in a garage.