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I like The Hamilton (www.thehamiltondc.com) for brunch. The food is delicious. Love the mimosas :) They also do a gospel brunch that I'd love to go to. I'm not sure if they're planning to be open on Christmas so you'd have to call.
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You should make sure these places will be serving brunch, but the following places are open on Christmas Day: Blue Duck Tavern, Georgia Browns, Cafe Dupont, and Urbana.
Also the brunch/breakfast at the Hay Adams is delicious and incredibly memorable, so maybe call and see if they will be open (they might because they are a hotel). It's not cheap but it's probably the best special occasion breakfast I've ever had.
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