Great Falls Park is closer to DC than Old Rag and is much easier to navigate. It has beautiful views of the falls and picnic areas - Nate and I visit Great Falls all the time and we definitely recommend stopping by! Bonus: This area is not far from Tysons Corner Mall if you are in the mood to go shopping.
If you are in the mood for shopping while you are in the Northern VA area, we definitely recommend Tysons Corner. There are two malls next to each other Tysons I, which has a great movie theater, restaurants, and moderately priced shopping. Tysons II Galleria is right next door and features J.Crew, Anthropologie, and high end designer shopping options (e.g., Burberry, Chanel).
If you are going to visit a Smithsonian Museum, we highly recommend this one! The National Portrait Gallery houses the Hall of Presidents portraits and the famous Obama portraits. In fact, there are a number of Smithsonian museums in the area to check out! Bonus: The Portrait Gallery is right outside of the Chinatown/Gallery Place metro stop and is a block away from one of our favorite restaurants, The Smith.
The National Mall is a great area to visit because there are so many monuments and museums along the mall - including the Washington Monument, The Capitol, National Museum of Natural History, Lincoln Memorial, etc. Bonus: The National Mall is a short Uber to the District Wharf, which has a ton of great restaurants to choose from.
Le Diplomate is one of the best French restaurants in the city and we absolutely recommend you stop by if you can. As a heads up, this is also one of the most difficult restaurants to get reservations at in the city - so book early!