St Simon and Tybee are the islands to head to. If you're into the historical stuff, Fort Pulaski is a good visit on Tybee. Kayaking on the inland waterways is good stuff around there. You can paddle out Tybee Creek to see the Loggerhead nests in the fall. The Crab Shack is good eats on Tybee too.
A few of my favorite watering holes are Molly MacPherson's (great Scottish pub), Kevin Barry's (old school Irish pub), and The Original Pinkie Masters. Between Oglethorpe and River St is where most of the tourist-y walking happens. Lots of historical sites, and all the squares. New Orleans-like in some respects. East and West River St is all cobblestone and good walking to different shops and pubs. That's where Kevin Barry's is.
You have to eat at Zunzi's. There won't be a lot of competition for seafood to what you're used to, but you have to eat Brunswick stew while you're there. If you can get out to Isle of Hope, Sandfly has the best bbq and Brunswick stew. I worked summers as a councilor on Isle of Hope at a Catholic camp run by the nuns when I was a teen. Pearle's is also out there, which is a great place for seafood and particularly crab. These barrier island produce wonderful crab. You can get some turkey necks, twine, a 5-gallon bucket and a net and go fishing for them yourself out on the marshes.
As far as peaches, South Carolina actually produces a lot more and better peaches. I'm across the Savannah river from Johnston, SC which is peach heaven. Unless, of course, you're talking about the other kind of Georgia peaches.
We take students onto Lady Jane's Shrimp and Dolphin Cruise every year. It's incredible. Basically, you go out on a shrimp boat through through marshes. There's a naturalist on board, and they drop nets and scoop up different species of fish and wildlife natural to the area. It's a really cool tour. Plus, just the boat and water part is great. It's in Brunswick next to Marshside Restaurant, which is also a great place.