Excellent choice.
For DC, I'd recommend trying to find a hotel where you can ditch the car there and hop on Metro. There's lots of hotels in DC that would enable this, as well as some in VA (around Crystal City or along the Orange Line corridor in Arlington). Any way you slice it, proximity to Metro is what you want. Though, the advantage with being in the city is that you're within walking distance of a lot of stuff and might not have to deal with the Metro at all.
Quite frankly, just about any place in DC that has a trusted, name brand hotel is going to be in a safe area of the city. Just as jmh notes with New York, so long as you're paying attention to your surroundings and not making yourself a target, DC is exceedingly safe.
There are also some great neighborhoods worth staying in as well, a little removed from the core of downtown. There are some hotels nestled in and around places like Dupont Circle that might be worth checking out.