Eh, to be honest, there are a myriad of brands you can buy in Gangnam/Apgujeong. There are cheap stuff like Stussy, expensive stuff like rare market, thrifting like VinPrime near Seolleung (i love that place, tons of excellent vintage finds, like vintage lee denim jackets, vintage americana, etc). And a very famous local brand called Unalloyed is also near Seocho/gangnam.

Otherwise not only gangnam, Itaewon has Mardi Mecredi (i'm sure you've seen this either in dramas or just on the streets in general), marithe francois girbaud, etc. If you are totally not into brand names then probably places in Dongdaemun like APM is more up your alley.