The best use of your time while visiting Savannah is to walk.  A great first walk is to start at Bay Street and Bull and walk south.  

You will pass through several squares, each one has different historical markers and a different statue or monument.

It is not a race, the south is depicted as slow, there is a good reason for that, it is often very hot.  Take your time, sit, look around, enjoy every square, each one is a different experience.  

When you reach Forsyth park (you will know it, it is huge)  take a few picture of the fountain, but don't stop!  Continue all the way to Park Avenue, at the far end of the park.  Maybe get a coffee at the Sentient Bean, or a juice drink at Brighter Day.  Now there is also th option of the new deli in the recently opened visitors center, near the playgrounds in the middle of the park.

When you are done wandering around Forsyth, walk east a block to Abercorn or west a block to Barnard and you have a brand new walk, with brand new squares, on your way back to Bay street!