I am from Northern Virginia and live only an hour outside of

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I am from Northern Virginia and live only an hour outside of Washington D.C. but I don't really know much about it. The National Gallery of Art is my favorite place in the world and I've been to some of the other museums but I'd like to get in deeper. I want to really get to know D.C. all sides of it. I'd be willing to spend a few days there but it's easier for me to just go home after a long day in the city since I don't know anything about leaving my car there overnight.

I don't care about food and I can't dance so restaurants and clubs naturally bore me. I want something interesting, I want to meet interesting people, and I want to eventually feel like I am from the city. I hope this is not too vague for me to get some recommendations. Also I'm thinking about trying to busk in D.C. I've done it outside of the country before and I'm at least competent on my instrument but I wouldn't where to play so if anyone has a good place in mind, I might try it.