Here's my attempt to answer your question, but I imagine there's more to your story as I haven't been in Georgia enough to explore your local weather patterns: First, most of those cities you listed are closer to the coast and will get more moisture. Atlanta seems to be stuck in between where storms finish picking up Gulf moisture and start tapping into Atlantic moisture if you imagine typical storm tracks. Obviously, if you can't get enough moisture, you won't have big snowfall totals.
The other big key is the start of the Appalachian Mountains to your north. If you have any winds coming from the north to northeast, you will get downslope flow off the mountains, which will make the air warmer and drier as the moisture is squeezed out over the mountains from upslope flow on the other side. The other cities you listed do not have mountains nearby that could create this problem.
Hope that provides you a better idea for your area. I'm sure there are plenty more, and you would have to watch approaching storms to see if you can spot more issues that inhibit your snowfall accumulations.
Hmm, I didn't really take that part into consideration. That could be a large reason why during the February 12, 2010 Snowstorm places like Columbia, SC for example picked up 8 inches, they may have been closer to the Atlantic to receive additional moisture from there. Something I did neglect to mention was dry air, in the past couple of years where we have had snow storms, an Arctic Cold Front swept through, sometimes as early as just the day before. I know the more dry air, the longer it takes for the moisture to saturate the air to the surface thus cutting into snow totals, but in these cases the Gulf moisture was heavy, heavy enough that once the snow fell it stuck immediately it would have seemed like those heavy snowfall rates would have been able to combat that period of virga and bring significant amounts of snow, but apparently not.
As far as the Appalachian Mountains, they can sometimes help us out with Cold Air Damming (or COLD Wedges as out local mets simply call them) ,but in those cases we need a stationary high to our NE (preferably around the interior NE/SE Canada) to flood the cold air down to us and since cold air can't go straight through mountains, it spills around on the NE side trapping it into the valley areas such as Atlanta for example. It could be argued in those type of events we would see more icestorms than snowstorms however because the cold air that gets trapped here is usually shallow in nature it can be overridden by warmer SW winds from the low pressure system to our South.
Going back to that question about storm duration, the only ones I know of that lasted more than 12 hours is the
January 2, 2002 snowstorm we had (Technically this was like two storms in one, an ULL dug in south in concert with a developing Gulf low enhancing precip/snow across our area) ,the
Superstorm of 1993 lasted about the same amount of time and I think the
SnowJam of 1982 was about 18-24 hours.
Also, snowfall amounts can vary across a big metropolitan area like Atlanta. While Atlanta officially recorded 4 inches of snow during the March Blizzard of 1993, some suburbs had 10 inches of snow. The totals can vary from one place to another.
You're absolutely right about that, I live literally only about less than 10 minutes away (by car) from the Downtown Atlanta area on the NW side of town and we picked up a foot of snow, I got baby photos to prove that. The suburbs I believe picked up more than that because I know in the mountains of N. GA they picked up about 3 feet. Unfortunately, what bothers me is that I feel that 4 inches is a terrible representation of what the majority of the city actually saw. With the airport being on the southside, they do tend to see less snowfall totals than the northside does, that is something I have always observed. It makes the saying about the I-20 corridor being a battle zone for snow or ice/rain fairly valid, it really doesn't help that the city is literally divided along that interstate.