The National Botanic Garden on the mall near the Capitol Bldg.; be sure to see the conservatory, the adjacent National Garden, and Bartholdi Park across the street. The Museum of the American Indian, next door, has great native American plantings all around the perimeter, and is worth a visit for the architecture alone. It's also my favorite place to eat lunch - their food court has representative foods of all the US regional tribes and is amazing!

The National Arboretum, to the Northeast of the mall, is expansive and definitely worth a visit, as are the Kenilworth aquatic gardens, esp. in summer.

Greenspring gardens in Alexandria is a great municipal garden, and they have a plant shop that features great deals on member-propagated plants. Also a great place to get gently used gardening literature.

All of these have websites - I know that's more than three, but I could go on...

bubba,
thank you for all the suggestions I will definately be looking up the websites.
Ariel