Cheap flights to Savannah recently found by travelers 1  *. $78: Baltimore to Savannah on Allegiant Air - nonstop (found 08/15/2016) 2  $127: New York City to Savannah on JetBlue Airways - nonstop (found 08/15/2016)  $365: Chicago to Savannah on United Airlines - nonstop (found 08/15/2016)