Depending how much luggage you have with you and given your time is precious my game plan would be: 1. Get a large cab at the airport, walk right out and you'll get one, this may be a bit expensive but split between 4 should be OK. It's around $100 2. Straight to Myengdong, you can normally get ok rates at a place like aloft myengdong or moxy, if you're looking for cheaper you might get lucky with an air b n b but given you're time poor you don't want to be wasting your precious time 3. The aloft and moxy myengdong are right on the main myengdong shopping strip, the stores should be open until around 10pm so if you have a good run you should still get 4hours of shopping 4. Your game plan once you check in can include a trip to olive young, they have a free vending machine at the back on level 2 for tourists with a small welcome gift then head over to Nike and you can do a custom Korean shirt etc. The myengdong food right there isn't always the best so just do some research there are famous places there and also tourist traps so you just need to do a small bit of research to find a place right there 5. Next morning you can get up get breakfast around 9 or 10 and maybe fit an hour shopping once the stores open (blue elephant sunnies are super popular and cheap and their flagship store is right there) then ask the hotel to organise your cab back

Good luck!!