Distrikt Bistro is the newish bistro in the JCC, 16th and O, a few blocks form the White House, very close to the convention center and most of the downtown hotels.
I've been twice. It's nice enough to go to with non-observant colleagues, but it's in a sort of wide nook in a public area of the JCC, so it has to go in the category of casual. But it has tablecloths, wine, and the space is pleasant.
And, the ting is, the food is really pretty good. You can check the menu, and see that it is limited. But there is always a special. The presentation is upscale bistro nice. They have the dishes prepped, so that even full meals arrive quickly.
On my most recent visit I had the Moroccan hariri, because I had had it on my first visit and it was so wonderful that I had to order it again. Glad I did. I followed it with the Dijon Roasted Lamb. Wow, simply wonderful.