There's a Holiday Inn in Rosslyn right across from the Key Bridge in Arlington VA that runs much cheaper than places in the city do, and it's a nice hotel
2k will cover museums (free), sightseeing, food (excellent food in the DC area), metro tickets, and craft beer/wine if you're into those things.
Obviously you're going to go the National Mall and see the Smithsonian museums, monuments, Capitol building, White House, etc... which is all 100% free.
The Zoo is really good and 100% free as well
I suggest going to different districts of DC every day to explore the city if you've never been there. Adams Morgan, Dupont Circle, Logan Circle, and Foggy Bottom/Georgetown are really must visits if you're younger.
You can also explore Alexandria and Arlington
Ive only been to DC as a kid, and I was too young to really appreciate it. Id like to go back and explore.
We were pretty close by last May, and planned on stopping there for a day. But it ended up downpouring the entire tome
If you do go that hotel I posted is my suggestion of where to stay. It's literally right by a metro station, and I think we paid like $150 a night in July to stay there.