It would be lovely to see the Smithsonian Gardens in the spring or early summer. Even with our late fall visit several of them were still stunning. There are sculpture gardens, a rose garden and a butterfly habitat.
The butterfly habitat was done for the season. We quickly walked through it and were hoping the rest of the gardens were not in the same state.
Most gardens surrounding the buildings are open at all hours, but a few are behind gates and open museum hours. More information can be found here: http://gardens.si.edu/plan-your-visit/
stretchingittotravel 
I remember taking my girls there in the 90s.
What lovely gardens.
Thanks for stopping by!