Will a 6㎡ room actually fit two suitcases and a person?

At 188cm with two large suitcases, 6㎡ is genuinely tight and worth planning around rather than discovering.

What a 6㎡ room typically contains before you arrive: a single bed, a small desk, a chair, a narrow wardrobe, sometimes a mini fridge. That leaves roughly 1 to 1.5 square metres of actual floor.

On the bed, which matters more for you than the floor: standard goshiwon beds are Korean single size, around 190cm. At 188cm you will fit but not comfortably, and some older buildings have shorter frames. Ask specifically — "침대 길이가 얼마예요?" — and if you can, view rather than trust the listing. A few buildings have a small number of larger rooms; ask if they have a 큰 방.

On the suitcases: they live with you. Most goshiwon do not have storage, and the ones that do usually have a small shared room where things go at your own risk. The practical solutions students use:

1. Buy soft duffel bags, unpack the hard cases, and collapse them under the bed. Most goshiwon beds have 20 to 30cm of clearance, which fits a flattened soft bag but not a hard shell.
2. Ask the operator directly whether there is 짐 보관 (luggage storage). Some have it.
3. Vacuum storage bags for off-season clothes. 10,000 won at Daiso and they genuinely halve the volume.
4. Luggage storage services exist near major stations for longer-term storage, around 30,000 to 50,000 won a month.

My actual recommendation for your situation: pay for the 8-9㎡ room rather than the 6. At your height the difference between 1.5㎡ and 3㎡ of floor is the difference between stepping around your life and living in it, and it is usually 60,000 to 90,000 won. Also filter for rooms described as 큰방 or with the size stated in ㎡ rather than just "single room".