Looks like I'm a little late but for BBQ I cannot recommend highly enough a place I call Emerald City (not sure what the real name is) but it is located in the Emerald City car detailing lot. They set up a tent and smokers every weekend. The spare ribs and chicken are incredible. It is on Bull Street, just north of Victory Drive.
Oysters? I'd go with Bonna Bella Yacht Club. It's on the water on Dutchman Creek, great views.
Bonna Bella Yacht Club
2740 Livingston Ave, Savannah, GA 31406