I've been living in D.C. for more than 6 months (not to mention my previous 2 years of graduate school) and the city still feels new to me. When I was in graduate school, I mostly hung around campus (American University), the back of Georgetown where there was a quite Starbucks that friends and I would study at and easily distract ourselves with the nearby movie theater, or Dupont Circle which was walking distance for my apartment.
I actually really like this way of getting to know a city. I already have areas that I know I want to explore more when the weather is better (Bloomingdale, Rock Creek Park, Woodley Park, etc) and I can easily stroll around rather than flinging myself from building to building in vain attempts to avoid being cold.
One good way to I've found to learn more about the city is through the various blogs. Two of my favorite are D.C. Foodies and DCist. As a serious fan of good food, I love any site that tells me where to get some. Reviews of restaurants are very on point but since I don't eat out often, I particularly love the posts about local markets and the great recipes that accompany these post.
DCist has a great selection of local events and news and overall happenings in the city. Last Friday night, a friend and I lined up for the opening of their annual photo expo at a non-profit gallery with donated wine and a cool DJ. Over a 1000 people showed up to be squeezed up next to each other in a tight space all in the name of supporting free local art!
Anyway...more to come on my D.C. discovery