Postal Museum is right next to Union station and honestly very cool. A true hidden gem.
Ubers from Union station are expensive but might be your easiest/ quickest option because the only Metro line at the station is the red line and it doesn’t go to the main tourist areas.
Or if you really like to walk and don’t mind heat and humidity, you can literally go out of the main entrance to Union station and the Capitol will be directly in front of you. Walk straight across the park to reach it. If you turn left at the Capitol, the Supreme Court is one block up. If you turn right at the Capitol, you’ll be on the national mall. You can do a good loop of the mall starting at the Capitol.
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