Section A is the one that puts you on all fours, right?
I think that in the immediate vicinity (if you don't include parts of Rock Creek Park, and maybe even if you do), the Billy Goat Trail is the nicest hilly hike, and Huntley Meadows Park is the nicest flat hike (although the Mount Vernon Trail south of the 14th Street Bridge - the part with the wooden plank bridge - is up there as well.
In 18 years of growing up here, and 32 years since moving back here, I've done 'em all (even rapelled once off Carderock - that first time leaning backwards off a cliff takes one hell of a leap of faith).