this should ABSOLUTELY play into your decision. it's something that i briefly considered then eventually disregarded when choosing a gap year job. i would also advise you not to move to DC, even though it's an amazing city.
i lived in VA my entire life and attended college there, then moved into DC for the last 2 years since graduation. after a lengthy and painful process, i have now been told (after labeling myself a Virginian on my primary) that i am a resident of DC (and therefore out of state everywhere). now all 4 of the schools i could have paid ~30k yearly to attend are now a cool 55k+, comparable to some of the highest private schools in the country. i have spoken with numerous people in financial aid with these schools about my situation but unfortunately none of them can help me. i also never changed my drivers license, voters registration, or any other official documents EXCEPT i file taxes in DC. you need to have all of these things to be considered a resident. exceptions apply to full time students and/or young adults who are listed on their parents' tax returns as dependents. however, anyone who has financially supported him or herself fully knows that letting someone else file you as a dependent means way less $$ in the pocket for you. i know some people who have gotten away with filing taxes illegally in VA while actually living in DC, but i obviously would not advise that.
sorry for the long response, but this has been a huge factor in my application cycle that i found it difficult to find information on before i applied. my decision on where i will matriculate is now likely different than it would have been had i chosen to live 5 miles away in Arlington. so be careful!
edit: forgot to note that there is no advantage in being a DC resident when applying to Gtown and GW. according to GWs stats and "desirable" criteria, i am a stellar applicant but they have shown me no love.