Looking at the racial composition numbers by precinct, then examining the primary results, there was a lot of variation in the results among white voters. Urban/rural, which is probably a proxy for income, was the driving influence.
In Charleston County Obama won all the precincts which are 99%+ white, some with a majority. These are all affluent areas, some very affluent.
Obama/Clinton/Edwards:
Sullivan's Island - 54%/30%/15%
Kiawah Island - 54%/30%/15%
Isle of Palms - 39%/35%/25%
Seabrook Island - 48%/36%/16%
Mt. Pleasant 16 - 46%/33%/20%
Mt. Pleasant 25 - 46%/29%/26%
St. Andrews 5 - 40%/32%/28%
Charleston 1/2 (the 'silk stocking' district) - 57%/29%/13%
As a check on the affluent white vote, I looked at virtually all-white precincts in some rural counties with little in-migration (and hence not areas of a lot of economic growth), and in none of them did Obama get even 15%:
Bay Springs (Chesterfield Co) - 4%/55%/41%
Cat Pond (Chesterfield Co) - 0%/16%/84%
Brewerton (Laurens Co) - 11%/39%/50%
Holly (Saluda Co) - 10%/55%/35%
Allens (Cherokee Co) - 8%/22%/70%
Cherokee Falls (Cherokee Co) - 12%/30%/59%
Wilkins/Metcalf (Cherokee Co) - 2%/33%/65%
He did a bit better in precincts in rural-ish parts of growing counties in the Upstate:
Gramling (Spartanburg Co) - 16%/34%/50%
Gowensville (Greenville Co) - 16%/40%/43%
Skyland (Greenville Co) - 19%/30%/51%
Tigerville (Greenville Co) - 19%/36%/45%
The picture in urban precincts in Greenville and Spartanburg counties mirror those in Charleston, with Obama winning:
Greenville 18 - 42%/24%/33%
Greenville 23 - 47%/26%/27%
Pine Street Elementary (Spartanburg Co) - 42%/30%/26%
I'll take a look at the results in Columbia and other areas, but I would bet the trends are the same.
Here's where the race by precinct numbers are located:
http://www.scvotes.org/statistics/by_counties_and_precincts