Looks like you've gotten a lot of feed back already, but I suppose I'll add my 2 cents being a former NYC resident.
If you're looking for a charming, quiet, and safe area that's still within walking distance of all the good stuff down town you may want to consider Wagner Terrace. You'll still be in Charleston proper, 10-15 minutes walk to upper king (a lot of the action) and the farmers market on saturdays. I have some friends who moved from DC and fell in love w/ the area for many of the same reasons you described.
Anyway, good luck w the search and if I can help answer any more questions about different areas, real estate or even local eateries nearby, am glad to do so.