Use the City's Free Downtown Transit or go on a trolley tour the first day you visit, so you'll get the layout of the squares and know where you want to return.  You can pick up free maps everywhere and you can also take a walking tour that day or night or a riding tour  like the HEARSE GHOST TOURS   (reservations required ) a Local and Tourist Favorite in a Modified Hearse all over downtown or a Haunted Night Tour offered by several Trolley companies. Even if you are here just for the night someone can take you around and show you what Savannah has to Offer.

The Telfair Museum was the childhood home of the Telfair Sisters and now is a wonderful Museum  is the place to go to learn more.  The Owens-Thomas mentioned below is a collection of the Telfair.  Check out thieir page for more Information.

The Owens-Thomas house offers tours , and they have a nice gift-shop.  Insider Tip:  Most homes that are open for tour also have gift-shops that are open without paying for the tour, such as the Davenport House, or Mercer House. Churches are also open for visits, don't forget  Mickve Israel  or The Cathedral Of Saint John The Baptist 

Shopping - City Market is two blocks of Shops and Restaurants, and has plenty of places to sit and relax.  River Street  is full of shops tucked in old Warehouses.  On River Street, there are the usual souvenir shops but also a couple neat artist co-op galleries. These galleries close at 5pm also, so visit earlier to see interesting assortment of artwork, photography, sculptures, jewelry, stained glass, etc. 

Bonaventure Cemetery is about 15 minutes from Savannah historic district - it is beautiful to walk around and photograph, expect to spend at least 2 hours.  NOTE: Clean portapotties available. Take water, it's hot! You don't need to pay a company for a tour, and they do free tours two times a month meeting at the cementery. There is no charge for admission to Bonaventure Cemetery, or for the free guided tours provided each month by the Bonaventure Historical Society