On a Saturday or Sunday morning, venture out to the Capitol Hill nabe and walk through Eastern Market. Dating all the way back to 1873, the market features food artisans, local art and a flea market selling various bric-a-brac.
Walk down Barracks Row on 8th Street and sample a house-made Pop-Tart or boozy milkshake from Ted's Bulletin.
Start waiting in line for dinner at Rose's Luxury, named the "Best New Restaurant in America" by Bon Appetit magazine in 2014. The restaurant doesn't take reservations, but that shouldn't dissuade you from holding out for its glorious small plates and impeccable service.
Spend the night at the Capitol Hill Hotel, which offers good deals and unbeatable real estate (plus free Wi-Fi).