Two key events happen around Fourth of July, primarily the large fireworks show on River Street [1], always on July 4, and also an impressive fireworks display from the Tybee Pier and Pavilion, which sometimes is on a different night. A nice bonus of the Tybee event is that sometimes you can look out over the Atlantic and see a similar fireworks display held on nearby Hilton Head Island, South Carolina, a few minutes away by boat (but nearly an hour by car).
Links:
[1] http://www.moon.com/destinations/charleston-savannah/savannah/sights/waterfront/river-street