Savannah is a bit lack-lustre shopping wise I found but both Prospector Co and Goorin Brothers are worth the visit when there. Tybee Island was nice too. Myrtle Beach will be a bit desolate at this time of year, most of it closes around now or the end of August, so I'd be inclined not to bother. Raleigh in NC is pretty good, having Lumina Clothing and of course Raleigh denim co. White Oak mills where 99.9% of American-made selvedge denim comes from is just up the road in Durham. Charlottesville also has a couple of old-fashioned menswear outlets, including "The Men and Boys shop" in the centre of town.
I'm very jealous, I loved the Carolinas and Virginia when I went in 2015. We took in Nashville and DC too, it was an amazing trip and we went in the fall too, albeit a bit later, towards the end of October. If you get a chance, the Blue Ridge Mountain parkway is stunning.

Thanks for tips Tim & WM, I'll be in Duluth, so hopefully I'll be able to check out H. Stockton.