The National Arboretum located in Washington DC is one of the best in the country. Some of the gardens/collections include: Asian Collections, Azalea Collections
Dogwood Collections, Fern Valley, Friendship Garden, Gotelli Dwarf and Slow Growing Conifer Collection, Holly and Magnolia Collections, National Bonsai & Penjing Museum, National Boxwood Collection, National Grove of State Trees, National Herb Garden, and Perennial Collections. Anytime of year is good but the azalea gardens in spring is immaculate.
Here is the website http://www.usna.usda.gov/