Go to the Visitor Center first and get one of their maps
There are many brochures and guidebooks that have a street map of Savannah, but none like the one provided for free at the Savannah Visitor Center on Martin Luther King Blvd. My experience was that the help behind the counter wasn't particularly helpful .. I don't mean attitude, just not extremely knowledgeable about Savannah. Perhaps they were volunteers just helping out. The visitor center is inside the rail museum which is also worth a visit.
Buy the 48 hour parking pass at the Visitor Center
Parking in Savannah is free on the weekends, but if you're there during the week, the best deal is the pass purchased at the visitor center which allows you to park free for 48 hours in any of the metered or public spaces.
Hop a Trolley Tour
We took Old Town Trolley Tours which we picked right at the Visitor Center. It's an excellent way to get an overview of the city, its famous residents (past and present), it's history, architecture and scenic setting. Tours leave every 20 minutes and cover most of the major sites in the city. Total tour runs 90 minutes but guests can hop on and off at 15 different stops. Price for us was $20 and the ticket was good all day - 9:00 am to 4:30.
Do a Ghost Tour
Savannah is the most haunted city in America. There are scores of houses, parks, cemeteries and squares that have reported paranormal activity of some kind. There are many different ghost tours. Because the city is large, the walking tours cover only a small portion and hearing can be difficult. However, a walking tour does allow close proximity to the site and a more personal link. With a driving tour, you see more haunted sites and get an idea for the enormity of places reported to be haunted. The Hearse Tour is fun and the drivers offer the "spooky ghost story" feel. This is good for those who like to be scared. The Historic Haunts tour by trolley includes more historic background and known legendary tales with the focus more on the story and less on the theatrics.
Visit the Cemeteries
Savannah's cemeteries recount its history with particular artistic flair.
Colonial Park is inside the city and is alleged to be haunted with numerous ghost sitings and apparitions. Laurel Grove Cemetery is on the East side of the city and includes the grave of Juliet Gordon Lowe (founder of the Girl Scouts) and James Pierpont, composer of Jingle Bells. This cemetery also has Baby Land which is a wide area, marked by wooden signs where babies were buried in unmarked graves during the early part of the 20th century when infant mortality was high and parents could not afford burial plots.
Do a Walking Tour
There's an excellent Savannah walking tour app for the iPhone. This is what we used. It takes you square by square. You can choose to do whichever ones you want, and take a day or several days. The Visitor center also has information on Walking Tours. You take in so much more on foot than by car or Trolley. We listened to the app dialog in the car while driving to Savannah. It gave a great background. Then we took the Trolley Ride. The next day we did a few squares on foot. This gives you time to notice the details.