Hidden away in the Enid A. Haupf Gardens between the Sackler Gallery and Smithsonian Castle, the Moongate Garden is a small oasis of calm. It's inspired by the much larger Temple of Heaven Garden, a Ming Dynasty (1368-1644) landscape in Beijing.
The centerpiece is a black granite pool with a small pink granite island and walkways. At two of the corners are round granite moongates.
The Moongate Garden is part of the Enid A. Haupt Garden at the back of the Smithsonian Castle, directly behind the entrance to the Sackler Gallery.
From the National Mall, go through or around the Castle. From Independence Avenue, just go through the gates. The closest metro stop is Smithsonian (Orange and Blue lines); L'Enfant Place (Orange, Blue, Yellow, and Green lines) is only a couple of blocks away. Depending on the day of the week and time of day, there's some on-street parking, but you'll have to contend with the usual competition for spots.
There's no problem using flash or tripods, and there's easy access. But they do close the gates overnight; the gardens are open 7AM to 7PM.