Look at Hunting Island, SC. We have gone down right after Christmas many times and had a blast. The weather was cool, but you are a Northerner, so you should be okay with the 60-70 degree weather during the day and 30s and 40s, maybe, during the night.
They have lots of bike trails, but several miles of undisturbed beach with millions of shells, starfish, sand dollars, sharks teeth and other ocean gems. You can get fresh shrimp about 1/4 mile from the state park most days - you can watch the boats go in and out and if you time it right, you can get the shrimp as it comes off the boat. They have a large pier about 1 1/2 miles from the campground to fish off of and a marshy area between the pier and campground where you can go crabbing.
We love it and try to go at least every other year. I think it is a pre-requisite to have a dog if you go to Hunting Island.
It is about halfway between Charleston and Savannah, (about 1 1/2 - 2 hrs) so day trips to each of these places is doable. It is about 30 miles north (on the roadway) from Hilton Head.
Another option is James Island County Park outside of Charleston. 12 minute drive into historic downtown (yes, I timed it and it was at 5 pm).
We also have gone to Gulf Shores, AL and we had good weather and 70 degree temps for a couple of days, but then it cooled off and it was in the high 50s and lower 60s.
These are our "go-to" places during the holiday seasons and don't want to have to drive forever. They are only 7-10 hour drives for us.
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