Depending on how you define DC area, spring Carlisle. https://www.carlisleevents.com/events/events-detail/index?id=spring+carlisle
• Jalopyrama is within an hour and a half of D.C. and would be well worth the drive. It's an excellent event. • There's an exhibit at the National Museum of American History called "America On the Move" that's about transportation in general. There's a small amount of hot rod-related stuff, but from a general automotive interest standpoint it's pretty cool. Here's a link: https://americanhistory.si.edu/america-on-the-move • Capitol Raceway is about a 30 minute drive and they've got your usual test and tune stuff on Friday nights. Nothing special in terms of the cars, but it's just a bitchin' old track and there's never a bad time to bring a cooler and sit in the bleachers. • If you've got a rental car and want to do a mini road trip, the Eastern Museum of Motor Racing in Latimore Valley, PA, is about an hour and 45 minutes from D.C. Really nice drive once you're north of Baltimore, and it's an excellent museum (some drag racing, lots of early Sprint stuff...just a cool place. Have fun!
Sodley, Go to the Jalopyrama. It's the best traditional rod/custom show on the east coast. The Smithsonian (Air & Space and American History) museums are the closest things to "car/truck related goings-on" downtown. If you have a ride, head out to the Udvar-Hazy museum (adjacent to Dulles Airport); where the Smithsonian displays its "big" stuff: https://airandspace.si.edu/udvar-hazy-center Generally speaking, DC isn't a very car-friendly town. Traffic & parking are problematic. I work there and ride the METRO every day.