Northern Virginia has always been closely tied with the nation's capital. This part of the state benefits from the history and the cultural aspects of Washington D.C., featuring famous museums, cemeteries, and the home of the first president of the United States.
Much of the north-eastern corner of Virginia was farmland until the period immediately following World War II, when government employment increased and the population around Washington D.C. began to grow. The area experienced another explosion in growth due to tech industry jobs in the early 90s. Today it remains one of the fastest growing areas of the country.
While Northern Virginia continues to expand, the region ranges from crowded planned cities with excellent shopping to soccer-mom suburbia, from ethnic neighborhoods full of authentic restaurants to the upper-crust style of the Hunt Country.
Washington Dulles International Airport (IATA: IAD)
Ronald Reagan Washington National Airport (IATA: DCA)
Leesburg Municipal Airport (charter and private planes only, no commercial service)
Baltimore/Washingtonal International Airport (IATA: BWI)
Route 95 to Route 495 (the beltway) toward Tysons Corner/Falls Church
Amtrak provides train service on a regular schedule between points north and Washington, DC's Union Station. Washington DC's mass transit (WMATA) provides service to Northern Virginia on the Blue, Yellow, and Orange lines.
From the south, Amtrak provides twice daily service from Newport News, Virginia with a last stop in Alexandria prior to arrival at Union Station.
Taking Metrorail might be your best option - there are many stations within the Beltway (near Washington, DC, in other words), including one that emerges right outside the Fashion Centre at Pentagon City. It is also the easiest way to enter Washington, DC.
Driving can be convenient, unless you wish to enter Washington, DC, or cross the Beltway in either direction. The highways (I-395, I-95, I-495, and I-66) are extremely backed up during rush hour. The "Mixing Bowl" (the intersection of I-395, I-95, and I-495 south of Washington, DC) is especially notorious. Attempting to travel by road between 2:00 PM and 6:00 PM on any weekday (and, for that matter, on a weekend) is strongly discouraged.
Arlington National Cemetery, Arlington, Virginia. Just across the Potomac River from Washington D.C., adjacent to the Pentagon. Closes at dusk. This national military cemetery includes John F. Kennedy's tomb and the house of General Robert E. Lee. Visitors can watch the changing of the guard ceremony in front of the Tomb of the Unknown Soldier. 
Old Town Alexandria, Alexandria, Virginia. This highly walkable Old Town at the edge of the Potomac River features historic buildings, churches, museums and art galleries, a farmers market, and a variety of places to eat and shop.
Mount Vernon in Mount Vernon, Virginia. George Washington lived in this country estate which overlooks the Potomac River. 
National Museum of the Marine Corps in Quantico, Virginia. Newly revamped museum displaying the history of the Marine Corps and their actions around the world. Features several aircraft, weapons, and interactive displays. 
National Rifle Association Museum and Headquarters in Fairfax.
Pentagon. Just across the Potomac River from downtown DC. While lingering is not recommended for security reasons, you should know it is the largest office building in the world, and covers 4 zip codes. (Army, Navy, Air Force and Department of Defense.)
Steven F. Udvar-Hazy Center - National Air and Space Museum, 14390 Air & Space Museum Pkwy., Chantilly, ph: (202) 357-2200. Located near Dulles International Airport, this museum houses many air/spacecraft, including the SR-71 "Blackbird" spy plane, the Concorde supersonic jet and the space shuttle "Enterprise". Parking is available for $12/vehicle. Additionally, a shuttle is available from the Air and Space Museum downtown. Prices range from $5 to $7 depending on number of tickets bought. 
Great Falls Park, in McLean. Gorgeous national park with waterfalls and hiking trails, minutes from the beltway. Kayaking and rock climbing. Going to the park after a large rain storm provides different views as the water levels can change drastically.
Fashion Centre at Pentagon City: A large shopping center with 170 different stores and restaurants. The basement contains a food court that has many different restaurants (including Panda Express, Villa Pizza, and Au Bon Pain). It is located near the Pentagon.