Alexandria can be kind of sketchy riding sometimes. I'd stick to the neighborhood streets and back roads. The main roads (Duke street, Route 1, Telegraph, Kings Hwy, etc...) can get up to 50+ MPH. Too much for me.
I'd suggest using the metro to get into DC. Once you are in DC, the riding is easier because traffic is so dense, cars don't get over 30MPH most of the time. Metro only lets bikes on during non rush hour periods.
Welcome to Alexandria!
BTW: Five Guys = In and Out Burger