http://www.si.edu/
They are pretty much sit around National Mall. Air And Space Museum is the most visited museum in North America.
The National Monuments, like Lincoln Memorials, Washington Monuments, etc, belong to National Park Service:
http://data2.itc.nps.gov/parksearch/state.cfm?st=dc
Smoky may get snow by December. However, driving by Blueridge Parkway will see the landscape change from the South to Mid-Atlantic.
Hope this is helpful.