It's Washington, DC. There's a ton to do, much of it free. Here's an excellent website that offers many, many options: Official Tourism Site of Washington DC | Washington DC.
Four major tourist sites do require free tickets: the National Zoo (pandas!!!!), the African American History Museum (awesome cafeteria), the Air and Space Museum, and the Holocaust Museum (there is a $1 transaction free for reserved tickets). For the most part, tickets become available 30-90 days out.
Your best bet is to take a ride share to the nearest Metro station as parking at DC tourist attractions can be challenging and expensive. The Metro is safe and easy to use, and you can even pay the fare with your phone (Apple Wallet or Google Wallet).
The Washington Nationals (MLB) and the Washington Mystics (WNBA) will be in the midst of their seasons. The Nationals will be playing Texas at home. There will likely be an evening game on Friday and a day game on Sunday. (The Orioles are away until the 10th.) The Mystics have home games on Thursday and Sunday for the WNBA Commissioner's Cup.
We hope (dream!) that the Capitals will be playing deep into the Stanley Cup playoffs. There's always the possibility that the Wizards will be in the NBA playoffs (and by possibility, we mean that Washington does plan to have an NBA team in 2025, and the NBA does plan to have playoffs). Oh, let's be real. The Wizards aren't going to make the playoffs, so you can just mark that off your list.
One unique "only in DC" event that we can highly recommend is the Friday Evening Parade at the Marine Barracks at 8th and I (Metro accessible). It's free and great for families. It does require sitting on bleachers outdoors for a few hours. There are lots of places in the neighborhood to grab dinner before or a drink after. More information and the reservation form can be found here: Friday Evening Parade (marines.mil).
If there's a specific attraction, event, or entertainment you'd like to know more about, please reach out to Chris and Mary at our wedding email address: sperryfederanichwedding at gmail dot com.