One of DC's true gems.
The Smithsonian museums in Washington, D.C. are open every day of the year except December 25. Unless noted otherwise, museums are open from 10am-5:30pm; the Anacostia Museum is open 10am-5pm, except during exhibition installation. The Smithsonian Information Center, located in the Castle, is open 8:30am-5:30pm.
[ Smithsonian: Hours ]
In fact I was at least 18 years old before I "discovered" that museums aren't usually free...
Disclaimer The opinions expressed herein are my own personal opinions.