Savannah's low season is around November through the end of January, and there are significantly better deals to be found, generally speaking, to compensate for the chilly weather.
For savings on dining around the city, look into the Savannah Menu Card (savannahmenu.com), which offers special deals such as a free appetizer or discount when presented at member restaurants around the city.
For savings on hotels, the site stayinsavannah.com offers discounts at member hotels. The best deals can be found during the off-season. Another way to save on hotels is to book a place south of the Historic District. There are a number of hotels along Abercorn Street, south of DeRenne Avenue, that provide easy access to downtown for less money per night.