In Alexandria --
Ft. Ward Park, W. Braddock Rd.
some trails, open space, historical, small playground
Dora Kelly Park (Near the Jerome "Buddie" Ford Nature Center), 5750 Sanger Avenue
Wildlife sanctuary, trails, stream, rocks, wetlands, and more
Winkler Botanical Preserve, Beauregard St. to Roanoke Ave. (looks like your going into an apartment complex, follow it to end - dead ends into the Preserve)
wildlife sanctuary, trails, ponds, stream, water fall (man made), and more.
And if you want to go a little further---
Roosevelt Island - G.W. Parkway South
trails and monument
Longbranch Nature Center and trails
625 S. Carlin Springs Road
Arlington, VA 22204
Huntley Meadows -
Nature Center, wetlands, boardwalk, trails, etc..