You can fly into Savannah and catch a cab into downtown, but you'll probably need a car if you want to explore attractions like Bonaventure Cemetery, Tybee Island, and Fort Pulaski, which are several miles east of downtown.
Getting to Savannah: There are a handful of direct flights into Savannah, but unless you're visiting from New York City, Chicago, or a few other major metropolitan areas, you'll have a connecting flight, most often through Atlanta or Charlotte.
More Flights: Although Savannah's airport serves both it and Hilton Head, there is another, considerably smaller airport on Hilton Head Island. If you're looking for additional flight options, it is only about 45-60 minutes from Savannah.
On the Ground: Savannah is about 10 miles east of Interstate 95, so if you're heading up or down the Eastern seaboard through Georgia, it is an easy stopover. Follow Interstate 16 east until it dead-ends in the Historic District. Interstate 16 goes west through Georgia to intersect with Interstate 75, the fastest route to or from Atlanta by car.
Other Options: You can reach Savannah by train; there's an Amtrak station several miles west of downtown. Bus travel is also an option. The Greyhound station is located on West Oglethorpe Avenue.
Renting a Car: There are several major car rental companies with offices at the airport, including Avis, Budget, Dollar, Enterprise, Hertz, National/Alamo, and Thrifty.