Apartment For Rent In Northumberland County Virginia . Search by city, state, property name, neighborhood, or address. 3400 potomac ave, arlington, va 22202. Top London & UK & Ireland & Scotland & Wales Weed From from londonweed.net 2 bd | 1 bath | 1,808 sqft. The median northumberland county, va rent is $8,750 which is above the national median rent of $1,469. $1,500 /mo apartment for rent.