I took my backpack to Washington DC. I had to empty it on the counter at the Smithsonian Native American exhibit, but they did let me in. I do carry a smaller pack, about 40Liter.
I had a long layover in DC en route to my backpacking trip in VA (summer 2014). There is a commercial bag check service at the train station, but it is very expensive and on-line reviews are horrid. But I found out that The National Gallery of Art (on the Mall) has a free bag check. Only certain entrances can check big bags - see link. I used the west entrance of the West building. I had to empty my bag so they could search it (I felt embarrassed making them do all that work, but they were very nice about it). I repacked everything and they put it on a rack while I explored the gallery. Now you are supposed to use this service just while you are in the gallery, but they can't really stop you from leaving and going to other museums on the mall. Admission is free so there is nothing to stop you from coming and going. Just make sure you pick up your bag before the bag check area closes or you could be in a real pickle.
Also, some of the Smithsonian Museums have lockers you can use. Many are small lockers that would not be big enough to hold a pack, but the Natural History Museum (next door to the National Gallery) had larger lockers that would hold my pack (although it's a relatively small Kalais - a big expedition pack may not fit). I also took the bus out to the Air and Space annex by Dulles Airport. They also have large lockers. It's a bit of a pain to get to by bus and takes a good part of a day, but I'm an aviation nut and had not been there before so it was high on my priority list. Doing these things I got to see the only DaVinci painting in the western hemisphere, the unbelievable annunciation by Van Eyck, an SR71, a space shuttle, and lots of other cool things.
http://www.nga.gov/content/ngaweb/vi...-policies.html
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It was the only time that I hid my backpack in the woods -- I bushwacked at least 1/2 mile into the woods (maybe more) to hide my backpack and chainlocked it to a tree and put some brush on top of it (a few backpacks had been stolen when I was on my AT thru-hike ahead of me so I took as many precautions as possible). It took about 15 minutes of looking after returning to the AT before I found my backpack.
The trip into Washington, DC was really fun on my AT thru-hike. A bit of a shell-shocked experience with all the people and noise but still lots of fun. The last time I had been to Washinton. DC before that was collecting on a $400,000 bill (todays dollars) that was owed to me (not fun but still quite a life story on the collection part).
Datto