On all sides of the National Mall there are Smithsonian Museums, National Monuments, The Capital Building and the White House. All Free admission. Recommendations: Air and Space Museum, US Botanical Garden, Holocaust Museum (if your in the mood).
Less then a hour away the Udvar-Hazy Center is a Smithsonian in Virginia that houses various planes, helicopters and other flying vehicles. It is the home of the Enola Gay and the Space Shuttle Discovery. Admission is free, parking is $15 per car before 4pm.
The Spy museum is a lot of fun. It houses the craziest spy gadgets and James Bond's Aston Martin. It is a private museum and is ~$25 per Adult ~$18 for seniors and military.
If the weather is nice Arlington National Cemetery would be a great place to visit. Changing of the guard for the Tomb of the Unknown Solider is a must see.
Seven mins up the road from the hotel, Yuraku is a really good sushi restaurant.
Ten minutes from the hotel, Thai House a great spot for spicy food.
Dogfish head is a Delaware brewery that has a restaurant six mins from the hotel. It is great for beer and a wide variety of food from pizza to burgers to BBQ.
Paladar is a Latin kitchen 8mins from the hotel. It features various Latin cuisine and a rum bar, including rum flights.
The Silver Dinner is a locally sources dinner that is great for breakfast and is opened until 1am if you are arriving late. It is ten minutes from the hotel.
First Watch is a great, very popular, breakfast and lunch spot, ten minutes from the hotel.
Ten mins down from the hotel Minerva has a great Indian lunch buffet. Go hungry!
Thirteen mins from the hotel, CAVA Mezze (not to be confused with fast casual CAVA) is a wonderful Greek tapas restaurant. A little pricey, but worth it if you are adventurous.
Founding Farmers is a very popular, farm to table restaurant 15-20mins from the hotel. If you visit DC there is a Founding Farmers near the White House, a Farmers and Distillers in Chinatown, and Farmers Fishers Bakers in Georgetown.
In the same town center as the Rehearsal Event venue is Peter Chang, an authentic Chinese restaurant.
In the same town center as the Rehearsal Event is La Canela, a upscale Peruvian restaurant.