While I don't have a garden center to suggest, you can try Fifth Season in Carrboro for organic seeds.... they also have organic fertilizers and such as well...and even aquaponics if that is of any interest.

There aren't really any "organic" per se garden centers in Durham. There is Barne's Supply on Ninth Street in Durham but they seem to specialize in horse supplies and specialty pet foods. They have plenty of bulbs and garden seeds/ plants but they don't gravitate towards organic. In northern Durham, there is Triangle Farms, basically another feed store that specializes in just that; feed. They sell veg plants and seeds aplenty but they know very little about what they sell. Its frustrating because they don't really seem to care about organic, but it is what it is. There are a couple other small garden centers but organic is the last thing on their minds so not worth mentioning.