There are a lot of excellent suggestions in this thread. If you have enough time, you might also visit Baltimore Harbor for a day. Baltimore is about 45 minutes from DC. It has some very nice places to eat, an aquarium with dolphin show, and several other attractions. There are water taxis to visit other nice spots, paddle boats, and during the summer there is usually some artist performing during the day. The USS Constellation is docked there as well as a submarine. There's a lot to see and do. Visit during the day, leave in the evening. I included a couple pics of Baltimore Harbor.
In DC, also visit the Spy museum - its pretty neat. Consider taking a boat tour. It will give you an opportunity to see the city and sights from a slightly different perspective. You can also take a nice dinner cruise. National Harbor is also a nice place to see, with some excellent restaurants and shopping. I live about 15 minutes from National Harbor.
I've lived in DC for about 25 years and have traveled all over the world. So, when it comes to crime, DC is like any other large city. There are places where you do not want to be after dark, but for the most part, DC is a safe place to visit. Mathogre's summation, "DC is broken into four quadrants: NW (northwest), NE, SW, and SE. Generally speaking, NW is the safest of all. I would advise staying away from most areas in the other three" is fairly accurate, but I would say stay on the West side (NW or SW) of town.
Have a wonderful visit. DC is an awesome city.
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