Seoul Beauty Trip — Which district do you all live in?

Hi everyone! I'm Huiwen from Taiwan. I'm planning a trip to Seoul this fall for a beauty treatment, and I'd like to do some shopping and relax while I'm there. However, I'm still a bit unfamiliar with Seoul's geography, so I'd like to ask for your experiences!

I've heard that Gangnam and Apgujeong have a lot of beauty clinics, so they seem to be popular areas for cosmetic procedures? But I'm not sure if staying there is the most convenient, or if it would be more cost-effective to stay in another area and take the subway. Has anyone stayed in these areas? Also, what's the safety and shopping environment like there?

I'll probably be staying for about a week and want to experience Seoul while getting my treatment. Does anyone have any favorite areas to share, or any tips? I'd also like to hear what research you usually do before your treatment! Thank you!