Which Smithsonian? They have like 14 museums, but I assume you are talking about the Air and space one. That museum alone is an all day outing however. I have been 3 or 4 times and there are STILL parts of it that I havent seen yet. I tend to get bogged down in the WW2 and Naval operations areas, so I havent been on the other end as much. I could probably spend a week in there.
And yes, they are open on Sundays.
As to what else you might squeeze in, of course there are too many things in DC to even list, but if its your first time, you should at least go look at the key landmarks such as:
Capitol, White house, Supreme Court Building, Treasury, Pentagon, Arlington Cemetery, Washington Monument, Lincoln Memorial, Vietnam Memorial, Marine memorial, etc etc the list goes on and on.
If you want to check out another Smithsonian museum, besides the Air and Space one, the 2d best in my opinion, is the Smithsonian museum of American History. This one is another all day deal, if you really want to do it justice.
