Flight
The two main airports to look at are Ronald Reagan Washington National Airport (DCA) and Dulles International Airport (IAD). Both are along metro lines and are easily accessible to Falls Church. DCA is slightly closer in distance, but you shouldn't go wrong with either. We'd recommend staying away from Baltimore/Washington International Airport (BWI) even if you can save a couple bucks.
Train
East Falls Church is your closest metro to "The Little City." Otherwise, Uber and Lyft are plentiful.
Hotel
Hotel
Hotel
Hotel