Stay away from Moon River Brewing. Bad beer, bad food, and bad service. Don't let the beautiful outside patio tempt you. The Distillery is always my go-to while in town for quality brews on tap and in bottle. They also have something amazing there called philly cheese steak egg rolls. World of Beer is just another World of Beer, but they have quantity to make up for what they lack in quality. Crystal Beer Parlor and Green Truck are good restaurants with decent beer selections.
Distillery was my go to as well when I was down there in February. Had a killer meal at Noble Fare, but they have a small beer selection. I was able to find a few local beers in the touristy district just by asking.
Check out the growler store while you are there, and the above mentioned options. There is also the bier haus, which had a lot of Belgians and other imports on tap. Unfortunately Savannah's beer scene is a bit weaker than you might expect, and even the good beer places can be a bit of a dissapointment in my opinion. When I was up there a couple of weeks ago, I did have a couple beers from a new brewery called southbound that seemed pretty promising though.
Habershams is pretty close to the historic district and is a fairly decent bottle shop, not sure if the will have stuff not distributed in NC, but its worth a stop.