Beaufort, SC would be a wonderful place for an elopement or small family wedding. It's a rustic fishing village with some outstandingly beautiful antibellum homes. The people there are just fantastic. They define "Southern Hospitality." It's in between Charleston and Hilton Head, making day trips to either very easy. Activities in the area include boating, fishing, birdwatching, you name it for nature activities, or you could just chill out at the waterfront park and do some shopping. They have some great little shops there.
It's a very small town and everyone is a bit "laid back."
There are 4 B&B's you should check into. They all have websites.
Beaulieu House at Cat Island - glorious seclusion!
The Beaufort Rhett House Inn - fantastic house
TwoSuns Inn - right on the Intracoastal Waterway
The Cuthbert House Inn - grand antibellum house
In case you're wondering, I'm from Charleston, SC. However, when I wanted to get away for a weekend, I would go to Beaufort. It's a bit like going back in time and doesn't have the tourist crowds of downtown Charleston or Hilton Head.
The Navy transferred us to Southeast GA, but we have a trip planned to Beaufort in November for the festival.
I would suggest early spring as the best time to visit for the flowers and outdoor activities. Early April is great for the dogwoods and azaleas. The magnolias will be blooming in May. Not being from the area, you should probably consider going in Spring before the bugs, heat and humidity get there.
Late Fall would be good as well, end of October or 1st part of November. By then the daily thunderstorms have pretty much subsided and there's less chance of a hurricane. I've done quite a few outdoor weddings (including my own), so I always consider the weather factor in any plans, indoor or out.
Hope this information helps.
