Washington, DC: Maybe the freshest air in D.C.
You may not associate fresh air and Washington D.C., since politics has a way of, to put it delicately, stinking up the joint.
But Dumbarton Oaks is one spot in the city that reliably offers tranquility and beauty. Located in Georgetown, the house was bought by Robert Woods and Mildred Barnes Bliss in 1920 and filled with their collection of Byzantine art. In 1963, Philip Johnson added a wing for their Pre-Columbian art. It is now owned by Harvard.
Go for the art, by all means. But stick around for the gardens. Originally designed by Beatrix Farrand, the original 53 acres have been split up a bit, but 27 acres remain as a public park and it is gorgeous from every corner and path and vista. At cherry blossom time (late March to early April), it's almost overwhelmingly beautiful.