Veazey Terrace is very close and an easy walk to the Van Ness Metro Station. I live nearby and would be happy to show this place to you. For more information please contact me at firstname.lastname@example.org or 202-494-0714.
You are steps from the Van Ness Metro stop. For your safety concern you should look into MPD` website, Washington Post or http://www.census.gov/ is a good source too.
From the cooperative at 3001 Veazey Terrace you can walk through the garages and into the grocery store. When you exit the grocery store you are exactly where the red line metro is. If the Giant is closed and you're walking on the street, it's between one and two blocks at the most.
For safety please look to the MPD's website.