Pete, you are going through a wilderness area on that stretch, so dockage is going to be pretty rustic. Choices are essentially Sunbury Crab Company (really a restaurant, but friendly and good food), Kilkenny Creek and Half Moon (hear those banjos?).
We took the big boat to Kilkenny once for a little "safety" fuel (I should have taken the time to fuel up in Brunswick, didn't want to detour and was headed for McClellanville SC for that). Mostly caters to smaller fishing boats, has a small store. Took the Whaler to other two, Half Moon is even more rustic than Kilkenny.
It is a shame you don't anchor because there area some of the most beautiful anchorages on the east coast along there: Walburg Creek, Wahoo River, Duplin River, Brickhill River and many many more. You might at least stop and drop a lunch hook and enjoy some of these spots only accessible by boat.
Here is a link to a handy guide:
http://cruisersnet.net/category/georgia/marinas-georgia/
We have stopped in Brunswick three times, each at the Brunswick Landing Marina, which is downtown. Picturesque southern town with good restaurants. The marina has some of the nicest shore-side facilities we've seen. Fuel up at Ocean Petroleum in the ship channel just before the marina; excellent prices, fresh fuel (it is a commercial dock a la Florida Petroleum in Fernandina), and very friendly, but dock is rough.
I also advise a short hop after Brunswick/Golden Isles to St. Marys, another lovely town. Either take your own boat over to Cumberland Island to explore (required anchoring-dinghy) or grab a park service ferry. Then another short hop to Fernandina. This area is worth lingering in and exploring before diving into urban Florida.
I'd be happy to walk you through the charts sometime; we are here in New Bern for the summer and perhaps the rest of the year.