Lunch near National Press Building?
I wouldn't say you can't go wrong with Old Ebbitt's but it does do some things right like oysters.
You could also try Breadline the sandwich shop on 19th and Penn, if you want something more low key.
I also don't think you are that far away from Ceiba, which is very good, or Galleryplace Chinatown which if you search on here has a ton of options.
My first choice would be Butterfield 9. They have a very nice lunch (go for one of the soups for an appetizer...they are always great).
Also there is an actual restaurant inside the Press Club Building. I believe its called The Fourth Estate. I've never been but the menu looks quite good (I almost went during RW but I had to cancel last minute).
Also not to far away is Bistro D'Oc.