Visit the Tomb of the Unknown Soldier and witness the Changing of the Guard. It’s solemn, beautiful, and deeply moving. Also, take in John F. Kennedy’s eternal flame. The Cemetary is next to where the chapel is located.
There are many historical battlefields all around the area that have hiking trails (over 40 miles of trails just for this one park), small visitor's centers, etc. If you want to brave the winter air and get outside, these are great ways to explore the outdoors with a side of history.
Always a fan favorite to walk, explore, and dine.
Beautiful grounds and buildings to see from George Washington! Quaint restaurant and gift shops.
Great museum, not "in the city" so depending on your transportation preferences, may be easier to get to.
Bundle up and take a winter walk past the Lincoln Memorial, Washington Monument, and WWII Memorial.
The Metro makes it easy to get into D.C. Download the WMATA (Metro) app to plan your trip and pay digitally. Uber/Lyft are abundant and relatively quick for short hops around the area (just keep in mind, if you are on base, you have to get off base to use one).