What saganista said. I would add only that there are many charming and unique neighborhoods in DC (Georgetown, Capitol Hill, Dupont Circle, Cleveland Park, for example) that, apart from Old Town Alexandria, really don't exist in Virginia, so a lot depends upon what you're looking for in a place to live. If you want the cheapest, safest, most convenient apartment, you're probably better off sticking to Virginia locations near your workplace. It's also much easier to deal with the local government (car registration, etc.) in Virginia, and Virginia has much better public services such as libraries, parks, pools, etc.
If you're considering graduate school in the near future, living in Virginia for 12 months would qualify you for in-state tuition at George Mason, U-Va, Va-Tech or other universities.