Yes, both the Hirshhorn and the National Gallery of Art have sculpture gardens. I remember the Hirshhorn's as pretty much just sculptures (several Rodins included); not much in the way of greenery except some small trees. I'll check the next time I walk past; it's just up the street from me, right outside the museum itself. Nearest Metro is L'Enfant Plaza's Maryland Ave & D Street exit (signage present inside station but not so easy to see).
The National Gallery's sculpture garden isn't co-located with the museum. The garden--which does have some large trees, at least, is located just south of Constitution Avenue between 7th St. and 9th St. It's straight across the mall (green space, not shopping) from the Hirshhorn, so the two can be visited together. Nearest Metro is Archives, I think. Both the sculpture gardens are very worthwhile from the sculpture standpoint, but you might be disappointed from the garden point of view.
The two sculpture gardens ideas are quite close to the Smithsonian castle and Arts and Industries Building, which I mentioned earlier. (Metro: L'Enfant Plaza or Smithsonian)
If you happen to be in that area on April 21 (Friday) and looking for quick food during the lunch period, there will be a fleet of food trucks along Maryland Avenue just east of 7th Street and south of Independence Avenue. Assignments shift every month, but there will be a variety every day.
If you have time and want a restaurant experience, there are some good places on and near 7th Street NW in the first few blocks north of Pennsylvania Avenue. This is particularly close to the National Gallery's sculpture garden.
I see you are from Minnesota, so I will mention our weather. April can be glorious, but in some years we have a 4- or 5-day period of unseasonably hot temperatures at some point that month. Keep tabs on the weather forecast before you head east so you'll know whether there are 90F days in your immediate future. I suggest cotton clothing, a sun hat, and a water bottle! And if the heat does kick in and by some miracle the cherry blossoms are still blooming down around the Jefferson Memorial, try to find time for the FDR Memorial as well. It's my favorite monument on killer-heat days because it has what I call "water features".
As your trip approaches you can probably find current info on the state of the blossoms by searching the Washington Post's website. You cannot judge by the date of the festival, because that is set ahead of time, based on a typically-inaccurate guess.