Baltimore:
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Ft. McHenry - A bit of a rip-off at $7 a head but if you’re a history buff you’ll like it.
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Aquarium - REALLY pricey but also just a fabulous aquarium. Worth 1 trip. Probably not a return trip.
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Inner Harbor/Fells Point/Fed Hill - Side-by-side-by-side districts of bars, shops, and piers that you can stroll about. Each has its own particular mix of boozy young professionals, boozier older non-professionals, and touristy-ness.
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There’s more to see, and it’s worth seeing but I’d say just set aside 1 day for Baltimore and hit the major points because DC/Va has more worthwhile sights.
Virginia:
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Udvar-Hazy Center. It’s an annex/hanger for the overflow of the Air and Space museum. That sounds worse than it is. It’s basically all the big stuff that you can’t logistically get into a small museum in the heart of DC. The Enola Gay, a lockheed SR-71, a concorde, the space shuttle Discovery are all there. Admission is free but parking’s $15. Worth it. Once, I think randomly, they did a special exhibit where they brought in local military/police/rescue helicopters.
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Old Town Alexandria - Right by the Potomac looking into DC. It’s got cobbled streets, ghost tours, and just about every building is a restaurant.
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Arlington Cemetery - It’s in Virginia an it’s weird to get to. I’d suggest you rent a bike and pedal to it if you’re physically able and inclined. It’s within pedal, or even walking distance from DC (the Lincoln Memorial), but it’s not exactly adjacent either. Probably 2-3ish miles.
Rosslyn/Courthouse/Clarendon/Ballston/Falls Church. These are the sequential stops on the Orange line as you leave DC. The farther you go, the more suburban the environment. Falls Church is about how far you want to go (and then south towards Annandale) for delicious, cheap, ethnic eats. Chinese/Indian buffets. Korean BBQ. Sushi. Pho. Schnitzel. Tacos. Pupusas. Kabobs. Schawarma. Pizza. Since you’re getting a rental car, I suggest that you eat a lot of your meals here. Yelp will tell you specifically which ones to hit up.
Monticello/Luray/Shenandoah - These places are far. Very far. In fact, Richmond is closer than these places and there’s more than just 1 thing to see in Richmond. I wouldn’t recommend these places unless you’re dead set on it.
Richmond on the other hand, has a delightfully underrated park (Maymont), a dangerously undersupervised Island (Belle Isle), Bobby-Flay-beating BBQ (Buzz and Ned’s), several civil war battlefields/museums/monuments/buildings, and one of the most accessible secrets in world-renown Chinese cuisine: Peter Chang’s. Oh, and there are breweries out the ass (Hardywood), but there are breweries and wineries out the ass all over most of Virginia in general. I’d say do a day-trip in Richmond if you really want to put miles on your rental car in favor of Luray Caverns.
DC.
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Zoo, yes. Best $0 you’ll ever spend on a zoo anywhere.
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Georgetown waterfront - Nice place to drop some coin on a delicious yet overpriced brunch and people-watch while you digest.
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Smithsonian. You can’t go wrong. Madmonk is right though, stay away from the American Indian museum, and gravitate towards the Art Galleries. There are 2 buildings (wings). The more modern building is smaller, and holds more modern art. The older building is massive and holds tons of art spanning time and cultures. There is an underground moving sidewalk that connects the two.
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Other museums, (moving from the capitol building end west towards the river) I would go to: Library of Congress, Botanical gardens, art gallery east, art gallery west, natural history, american history. Yes, I left out air and space, but if you won’t miss much IF you go to Udvar Hazy. Spirit of St. Louis, some WWI/II biplanes, the lunar module, and about 5000 of the loudest, stickiest kids you’ll ever hope to encounter. Yes, I also skipped the archives because the exhibit(s) is sparce.
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Off-mall museums. Right next to Union Station is the post office museum, which is NOT to be confused with the old post office building. The building is tall and you can go up, but the museum is a museum. Across the street from the Chinatown metro station is the national portrait gallery which holds even more art. Not many people go there because it’s off-mall but it’s just as good imo as the main galleries. There are pay-museums like the National Building museum, the Newseum, Holocaust museum, and the spy museum that are also worth it, but aren’t as good as the Smithsonian ones and yet are at a financial premium.
Past the museums are the monuments. Korean, WW2, Washington, Einstein statue, Vietnam, MLK, and the Lincoln Memorial. Once you get to the lincoln memorial you can continue east/southeast to the tidal basin which is a loop in which is the FDR memorial, the jefferson memorial, and the cherry blossoms.
Keep walking (if you’re not dead) and you’ll get to the fish market where you can get a quick bite, or just make note that DC has a fish market. There’s a Phillipp’s seafood buffet and some yachts tied up there too.
Famous DC “must-eat” is called the half-smoke from Ben’s Chili Bowl where many famous african american celebrities like Cosby and Obama have eaten. It’s good and even with the hype, it’s within budget.
Others? Arboretum (it’s a drive into the not-so-nice part of DC though). Dupont Circle (bars, restaurants, and just about every one of them has a great brunch option). Embassy Row (a lot of them hold open parties where you can buy a ticket for $30-$60).
And hiking. Great Falls (MD side) is a phenomenal hike. It’s also called the Billy Goat Trail. Great Falls (VA) side is merely a good hike. Both go along the potomac and has good views of the river before it reaches DC proper and eventually the Bay.