DC has a lot of pros/cons. I've been here 4 years and as a non-trad, I have gone from the young, new Washingtonian to the married living away from the main action life. I feel like I've seen a lot of sides of DC.
DC is one of the most expensive cities in the country, and GW is one of the most expensive med schools when you factor total COA. If I remember from my interview day, it's something like $90k per year in COA, but could very easily be more. You likely won't be able to afford your own place unless it's a depressing studio in a not-so-nice neighborhood, so you'll need to get roommates or live in a less desirable part of town. But the good/bad news is that gentrification is running rampant and a lot of neighborhoods are undergoing transformations and will soon be nicer to live in. You always have to make compromises in DC housing and the market moves fast.
The metro is the literal worst, don't even get us started on it. Traffic is miserable, and I've lived in other big cities so this isn't small town talk. If you have kids, the schools are the worst in the nation (trust me, I was a teacher here and this is statistics, not hyperbole). If you bring kids, you likely won't be able to afford the areas with the decent public schools so you'll compromise by living in VA/MD or private schools ($$$$$).
All that said: I'm a jaded Washingtonian most days. But when I sit back and look at the city, I love it. We got married here and took pictures with national monuments in the background. I've run into several members of Congress at the farmer's market (and even got brave enough to say hi to Rep. John Lewis at the cheese counter!). If you're tuned into politics - or want to be - DC is obviously the best place. Interested in health policy? DC is awesome. You're literally in the center of power for the country, and some would say the center of power for the world. The museums (most free!) are incredible and the food scene is pretty good, though always crowded.
DC's demographic makeup is interesting, and you'll definitely see the top of the 1% and the very bottom of the 99%, juxtaposed with the lawmakers who support/condemn that situation. DC is still a land of taxation without representation, so that's always interesting when Congress controls the budget but we don't have an elected representative with voting rights... Lots of history and historic race tensions here if you're interested in history/current social movements. Corruption in local government, like most places. It can be violent. I was caught in the middle of a drive-by shooting once leaving work.
DC is somewhere I never thought I would live, but hey look at me now: I'm staying for 4 more years.
Give me specific questions and I'm happy to respond.
