Try the Oglethorpe Trolley Tour, they'll pick you up at downtown hotels & take you to Visitors Center, where you take a narrated tour for 90 minutes that will drop you off at City Market and you can on/off ride their trolleys to selected stops for rest of day for $10/person - great deal!  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.  NOTE: if you're interested in history of homes around the squares and want to do your own walking tours, get a copy of "Sojourn in Savannah" - it's the official guide and map of historic Savannah that tourguides study for their tests.  Can buy it in several giftshops or on Amazon.com. 

The Owens-Thomas house offers tours for $8/person AAA rate & they have a nice giftshop.  Insider Tip:  Most homes that are open for tour also have giftshops that are open without paying for the tour, such as Mercer House.

Shopping - City Market is small, with OK shops. One shop worth noting is Nature's Treasures.  The shops here close at 5pm.  River Street Marketplace is full of local(?) vendors selling tacky stuff at high prices.  On River Street, there are the usual souvenir shops but also a couple neat artist co-op galleries close to Savannah Candy Kitchen. 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!