Hi Anna,
I was raised and currently live in the Maryland suburbs of DC. I only went into the city for specific occasions while in school, but now as an adult I work there part of the week, and my sister lives there.
Here are some random memories from my experiences:
- hearing the animals at night from the nearby zoo when you are just walking around in the commercial area nearby (Woodley Park)
- walking the long walk back across the 'bridge' from Adams Morgan to the Metro with my friends on a warm summer night after feeling like such a grown up for going to the bars.
- Eating astronaut ice cream at the Air and Space Museum
- Watching the July 4th fireworks on the national mall
- Spending part of prom night having our limo driver take us to the Lincoln Memorial
- Driving across the bridge back to Virginia at night and admiring all the lit up monuments
- The architecture of the Metro stations is beautiful, though the system itself has gone down hill in terms of reliability. Some cars smell like mildew before the doors even open. But they are heavily commuter trains. You don't see begging on the trains very much at all like you would in NYC. People don't make eye contact, they sit or stand and read their newspapers or e-readers.
- Passing buildings with interesting architecture and realizing how many of them are government buildings
- My grandmother was a docent at one of the art museums, so I have fond memories of them
- Sitting and eating lunch in Dupont Circle
- Eating Ethiopian food for the first time (there is a large Ethiopian diaspora here) and marveling that you eat with your hands
- Seeing traffic grind to a halt as a vice presidential or presidential motorcade goes by
- The Cherry Blossoms, as others have mentioned
- Seeing a show at the Kennedy Center
- Seeing the staircase from the Exorcist in Georgetown
- Driving down embassy row and admiring the buildings and trying to identify the flags
- Going with my coworkers down to the mall to watch the arrival of the space shuttle as it circled the monuments on the back of a 747.
- Participating in political rallies or protests.
- Going to a Capitols or Nationals game.
- Seeing a play at the Arena Stage or Ford's Theater or Shakespeare Theater.
As for the 'real dc', yes, there's a physical separation between the touristy parts and areas where people work, versus the more residential neighborhoods (with varying degrees of diversity and safety), but I wouldn't say people here make a 'real' vs. 'not real' distinction. Unless you're hanging out at someone's apartment or going to a specific bar or restaurant or thrift shop, there's not really reasons to get insider 'tours' away from the touristy stuff.
There are spy tours and things you can sign up for, where they'll drive you around and show you alleged drop-off points, or places where, say, Deep Throat was, etc.
I don't know if this is the kind of stuff you're looking for