There are lots of museums and monuments in DC. Many of them are free (although some may still require reservations). Some of our favorite museums include the National Portrait Gallery, Museum of American History, Museum of Natural History, and the National Gallery of Art. As far as monuments and memorials, the Jefferson Memorial, Lincoln Memorial, and Washington Monument are among the most well-known, but there are many others near the National Mall, including the World War II Memorial, FDR Memorial and, one of the newer attractions, the Eisenhower Memorial. We recommend driving to the Shady Grove Metro station and taking the Metro into the city. DC is very easy to get around via Metro, and the National Mall area, where many museums and monuments are located, is very walkable.
This is the shopping center where the hotel blocks and the rehearsal dinner are located. There are many stores and restaurants in this area that are walkable from both hotels.
There are plenty of nice places to hike or walk around in the area. Great Falls (https://www.canaltrust.org/pyv/great-falls-overlook/) is an easy walk and the Billy Goat Trail (https://www.nps.gov/choh/planyourvisit/billy-goat-trail.htm) is a unique hike.