I grew up in DC, lived in the area about 30 years and agree on timing. Mid-April to Mid-May is a wonderful season. The cherry blossoms bloom in the spring, though it is hard to time the right week, because it depends on each year's weather. October is great, with autumn colors. Summer is hot and humid.
The Smithsonian is wonderful but there are many museums, so do a little research in advance to decide what you want to see. The Air & Space Museum and Holocaust Museum are very popular, for example.You may want to look into a tour to get an overview of the city and monuments for starters.
History wasn't my favorite subject either, and now when we travel, I am finding the sites make it come alive. You might like Thomas Jefferson's home Monticello, Colonial Williamsburg, Jamestown, all in Virginia.