I don't know how good they are with men's clothes but the Opportunity Shop at the National Cathedral might have some nice stuff as its in a wealthier area, though if I had to guess, I'd assume there's more women's stuff there, but I really don't know.

If you' wear a size 17ish, a customer at my job gave me some white button down shirts around that size. You are welcome to them if they fit you. He offered and I took them, but I am only going to keep maybe one of 5 as I don't really need any more button down shirts so I'm happy to give them to someone else.

All of those places except for maybe theOlive Garden are not far from Metro stations in DC proper, I wouldn't say its worth (edit- it for a tourist) taking the Metro to go to them, but they are available.