Mido hotel is situation in the station right between Myeong-dong, I would say it's a prime location. There're also a few restaurants and a convenient store outside of the hotel. I must also reveal there's a lift to the level to the subway station!! Of course you still need to carry your luggage, walk the stairs to the track but using the lift will enable you to walk much less staircase :) If you are taking the bus from the airport, the stop to get we off is Namdaemun Market street.
There was no hot water supply on the last day of my stay. I used cold water to shower (just half shower, can't be whole body). My flight is 4hrs flight time so I can wait until I get home. But I know it could be hard if it happens during a vacation especially in December.
One thing I have to especially point out and compliment the front desk staff, the morning shift one in particular, they helped me to contact the airport bus operator and locate the luggage I left on the bus. The extra effort and attention is something I highly appreciated. To be honest, because of the hospitality and helpfulness of the hotel staff, even if there's no hot water, I would still recommend tourists to stay and I, myself, would like to stay there again. Because, as a solo traveller and in a foreign country, their great attitude to look after you certainly is a tremendous asset.