aly-ona

I had it at Seoul Queen. It's not that popular among foreigners, but I saw good rhinoplsaty reviews about them on their cafe + other apps.

 

I also agree with @yunggrandpa that you should look for B&A pictures to see the style of each doctor, and then decide where to have the surgery.
I narrowed it down to several hospitals, and then I went for the face-to-face consultation to these hospitals.

 

You should have an online consultation with all the hospitals you are interested in, look for their insta, blog, cafe, homepage, etc. to see more B&A pictures, and then I think it is better to decide where to do.
Also, when you have the consultation you can tell them you budget, and see if they agree to it or not, or during the face-to-face consultation you can ask if there is any event that you can apply to get a lower price.
Or just ask "Can you make any discounts?" and see what they answer.

I'm a half Korean, so I contacted the hospitals in Korean, and I think I got the price for the locals, but still for eyes and nose (just silicon and tip plasty, not any correction procedures like hump or crooked nose), I got somewhere less then $4000, so I think you can have the procedures within your budget.

 

If you are going only for PS, I don't think it's worth the trip right now..
You'll have to stay 2 weeks before surgery, and around 1-2 weeks after.
If you plan on staying for a longer period of time, then Korea is a pretty safe country right now.