One of the best things to do in DC is to walk around the monuments. From the Washington Monument, to the Lincoln Memorial, to the Jefferson Memorial or even the Theodore Roosevelt Memorial there is so much to see. You could spend an entire day just walking around them, or just pick one or two to look at on a night out. One of my personal favorite things to see, is the the Lincoln Memorial at dusk, then sitting at the World War II memorial and watching the sun set. Another favorite is just sitting in between the columns at the Jefferson Memorial facing the Potomac. There are so many options that you can do either with friends or even on a date.
For more ideas on what there is to see at the monuments, check here.