Arlington has become so great for bicycles that I don’t feel like I have to do anything special to arrive by bicycle. I think “what suits my fancy?” to pick a destination, I look it up on Google, take a quick look at my Arlington bike map and then start pedaling.
Lubber Run Park has a great amphitheater where they do live performances on summer evenings: http://www.arlingtonva.us/departments/parksrecreation/scripts/parks/LubberRun.aspx
BonAir Rose Garden is still in bloom. It is located right off the W&OD trail in Arlington.
Gravely Point is a great place to sit back and look at the underside of airplanes taking off and landing at National Airport.
One of my long routes home is through National Harbor (Maryland). I know that is a bit ridiculous… to ride from the White House to Falls Church via Oxen Hill, Maryland, but the ride through Old Town Anacostia and South East is enjoyable, I’ve had no trouble with traffic… even when there are a lot of cars on the road, and it is nice to have a bite to eat in National Harbor before crossing the Wilson Bridge and heading back via Arlington’s wonderful bike trails.
enjoy!