Ronald Reagan Washington National Airport (DCA) is on the Metro line, and it is simple to connect to the Red Line out to Shady Grove, from which a taxi will take you to your hotel. Rental cars and cabs from the airport are also available.
Washington Dulles International Airport (IAD) is in N. Virginia, and cabs and rental cars are typically used from there. It is possible to get a cab to the Vienna Metro stop on the Orange line and make connections to get to the Shady Grove stop on the Red line.
Baltimore/Washington International Thurgood Marshall Airport (BWI) is the farthest but can be the cheapest. Getting from BWI to NIST without a rental car can be complicated, but you can take the MTA train from the BWI Parking stop to Union Station in DC, then take the Red Line Metro out to the end at Shady Grove. It is a short cab ride from that stop to the area hotels. Newly available is the ICC Bus, which picks up at BWI and uses the Intercounty Connector (ICC) toll road to get to a park-and-ride lot that is 5 blocks from the NIST front gate and an easy cab ride to hotels.