First time going to Seoul! Anyone have recommendations for must-try beauty experiences?

Hi everyone! I'm Pei-Chun from Taiwan. I'm finally making my Seoul trip happen, and this time I'm especially keen to experience Korean beauty culture and skincare. I've heard Seoul has many amazing places for facials, skin management, and the like, but honestly, I'm a bit unsure where to start.

My skin is on the sensitive and dry side, so I'm a little nervous about new treatments but also quite excited. Has anyone been to Seoul and had any memorable skincare or beauty experiences? I'd love to know how everyone chooses clinics or beauty centers, and if there's anything I should pay attention to. I don't have a specific budget limit, but of course, I'm hoping for reasonable prices too.

Also, are there any particular beauty or shopping districts in Seoul that are great for browsing skincare products at the same time? I'm really looking forward to hearing everyone's suggestions! Thanks! ~