There is no way I would even drive through DC non-stop, let alone stay there with my weapon. As for carry, there are better ways to commit suicide!
Look into a nice hotel in Rosslyn, VA. It is right across the river from DC, only 1/2 mile from Georgetown, and about 3 miles from the Mall. There is a metro station in Rosslyn and can take you to any of the sights you might wish to see.
Virginia is just about the polar opposite of DC as far as gun rights are concerned.
Google search... http://www.google.com/search?q=rosslyn+va+hotles&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-USfficial&client=firefox-a#sclient=psy&hl=en&client=firefox-a&hs=zV2&rls=org.mozilla:en-US%3Aofficial&q=rosslyn+va+hotels+near+metro&aq=1& aqi=g2g-v3&aql=&oq=rosslyn+va+hotels&gs_rfai=&pbx=1&fp=9be f8cda26d1a6ec
Edit: Forget to stress this... when you leave VA to visit DC, leave the firearm locked up in VA.