Have done a fair amount of running there through the years and have yet to find a good spot; was there last week and even more land has been developed. Coastal Carolina U. is a nice place to do track workouts; it is about 15 minutes from town on 501. Nice track, or it was three years gao.
My distance runs during biannual family vacations there were always spent in the following ways:
1) Running on one of the 120 golf courses there before golfers are out (start by 6 a.m.) or after they are off the course at night. I stayed near 68th street and there is a good one just across Kings Hwy there that they don't hassle you about if you get on it around 8 p.m. I used to do two loops and finish with a few more miles on the beach.
2) Running on the streets parallelling the beach against the wind (so you don't notice it the way you would on the beach) and coming back on the beach WITH the wind (makes you feel fast).
3) Supposedly there are two state parks south of the city that are decent, but I have not tried them.
Bottom line: it ain't fun, but there are tons of ladies on the beach you can check out if you are into that while you cruise by at 6 minute pace.
At the beach I always just tried to get 12 miles a day (8 easy miles a.m., 4 miles quick in the p.m. or vice versa, bagged the long run and did one ball buster on the track and called it a vacation week). Just try to maintain while you're there, because it won't be a fun week.
Brian