The first one that comes to my mind is Johnson's Garden Center on Wisconsin Ave.

Here is a link that might be useful: Johnson's Garden Center

I would say the garden district is more what you are looking for in terms of standpoint.

"City Paper names Garden District best Garden Shop in DC" http://www.washingtoncitypaper.com/bestof/2008

(202) 797-9005
info@gardendistrict-dc.com
1801 14th Street, NW (Map)
Washington, DC 20009

American Plant strives to be organic.

I don't know how organic they are or strive to be, but American Plant (formerly American Plant Food), with 2 separate locations on River Road in Bethesda, is a very nice smaller nursery and carries a good mix of ordinary and more out-of-the-ordinary plants.

Garden District is good but TINY and has a fairly limited supply. They did recently open a second location just down the street, where they offer more pots and other non-plant supplies. Very much an urban nursery, but there are a lot of other interesting shops on that stretch of 14th St. so it might be worth checking out as part of a general shopping trip.

Also check out Ginkgo Gardens in southeast DC, another urban nursery but a bit bigger with a surprisingly good selection of plants and supplies. Just a few blocks away, Frager's Hardware has a good selection of plants & gardening supplies. Both are just a few blocks from Eastern Market and worth a visit on a nice Sunday morning in the spring.

Outside the city Behnkes, with 3 locations in Maryland, is one of the biggest local nurseries and a great source of gardening supplies and plants of all kinds, including trees and shrubs. However, despite their huge selection of plants I've had trouble finding anything there that is especially unusual in recent years.