As usual, I'm late to the game. But that won't stop me from sharing redundant information that has already been decided (well, maybe).
1. Yes, count me in (as long as it's not on a date when I'm traveling for work--I travel a LOT).
2. You can get much cheaper hotels in the suburbs and then take the train in (VRE, with stops at places like Crystal City, L' Enfant Plaza and then Union Station and Metro stops at them all). Like you could actually stay in Fredericksburg, VA and shoot the battlefield there and the old town then take the train in the next day.
3. If you're coming from NYC, I recommend one of the buses like VaMoose or Megabus. I've seen roundtrip tickets for $30, you get wifi, lots of space for tripods and/or Pelican cases.
4. Some suggestions for options to consider:
--night shoot of the Lincoln Memorial (from the back of it on a clear night you can see the Eternal Flame at JFK's gravesite in Arlington National Cemetery across the River), the US Institute of Peace (2 blocks away), the Einstein Memorial (across the street) and Vietnam Veteran's Memorial (across the street from the Einstein).
--Arlington National Cemetery, Section 60 (where the Iraq and Afghanistan dead are buried). People leave momentos on the headstones (see the photo below). You also have the Tomb of the Unknown Soldier and the changing of the guard.
--National Gallery of Art, East Building (contemporary and modern art) is speed light friendly and free. Great architecture and art that lends itself to creative abstract photography (like...shooting Calder mobiles).
--Hirshhorn Museum (more modern and contemporary art in a nifty space plus an outdoor sculpture garden).
--US Botanical Gardens (diverse ecosystems, the orchids may still be blooming if it's an early spring, they give out permits for tripods, and it's next to a bunch of other good stuff to shoot).
--Renwick Gallery (part of the SI but not on the National Mall, it is known for lots of large installations that make fascinating photographic possibilities and all galleries are photo friendly).
Everything I've just listed is free. Don't plan on parking on the National Mall. Take Metro, or Lyft, or park elsewhere and walk in. And b/c March and April in DC can alternate between "wow, it's summer already?" vs. cold, blustery, and rainy, I suggest that people have an indoor plan and an outdoor plan. Last thought--it's not very photo-friendly and it costs to get in but if you are interested in photojournalism and telling stories with photographies, when you're in town you should make time to visit the Newseum. It's worth the price of admission just to see the exhibits on 9-11, specifically the story of the "Falling Man" photo as well as Bill Biggart (who was shooting at the base of one of the towers that day and his crushed gear was found in the wreckage...and the photos were salvaged). Powerful stuff.