How do I fly from New York, New York to Hiltonhead South Carolina?  
What airlines take me direct?

Dear Annie, 

According to the Hilton Island's official website: 

"Hilton Head Island is served by:
Direct commuter flights to Charlotte via USAirways Express.

Savannah/Hilton Head International Airport provides:
Less than a 45 minute drive to the Island
More than 40 daily departures via USAirways, Delta, Continental
Express, United Express, COMAIR/Delta Connection, American Eagle,
Atlantic Southeast, Northwest Airlines & Air Tran
Direct flights to New York, Newark, Chicago, Washington D.C., Dallas,
Houston, Cincinnati, Cleveland, Detroit, Atlanta and Charlotte
All flights are met by ground transportation companies that can
transport you to the Island
Rental cars at the airport that enable you to drive to the Island " 

Of those airlines, Delta operates 3 daily flights to LaGuardia
airport, and 2 daily flights to JFK.
(See: Savannah Airport Commission Homepage,
<http://www.savannahairport.com/airlines.php>).

I hope this answers your question. Please contact me if you need any
further clarification on this answer before you rate it. My search
terms were :
"hilton island sc" 
"Savannah/Hilton Head International Airport"