If you can see something different and want a historic mansion, you could also consider the following:

George Mason's home, Gunston Hall, is only a few miles south of Mount Vernon. While the grounds are not as expansive, the house tours are always good and it is never very busy there. Seeing the Mason home provides some really interesting historical context for the Bill of Rights, and as Washington's neighbor you can see his influence. It's not really a full-day trip in the way that Mount Vernon is but I enjoy visiting occasionally.

The Hillwood Estate isn't tied to US history, but it has an excellent collection of art inside the mansion belonging to Marjorie Meriwether Post, cereal magnate and namesake of the Post Pavilion in DC.

Dumbarton Oaks also isn't really US history but this estate has a fabulous collection of central and south American art as various Byzantine pieces.

There are always the Smithsonians as well but I'm assuming you're well aware of those, figured I'd give you some other ideas.