I have lived just outside Seoul in Songtan. Are you relocating as a civilian or with Armed forces? We were with DH's job (he is military) and although we lived off base we had the benefit of a few extra facilities. We have done the moving half way across the world a couple of times now so am getting used to it.
Seoul is an interesting place to be though, have you visited before? It may all be quite a huge culture shock. But although the culture there is quite alien to ours it is welcoming and there are loads of cool things to see and do.
Are you moving your belongings too? At the bare minimum I'd advise you at least bring your beds. European beds are very different to Korean ones, which are super hard. A slab of granite with a sleeping mat hard. Honest. Even the ones that look like a divan have that granite slab feel!
Korean homes are very different to what you would expect here. Most people live in Apartment blocks. Most nice apartment blocks and even neighbourhoods are owned by companies. There is for example a Samsung are of town, an airport workers village etc. People live with great pride in thier company's blocks. Individual family homes are much rarer to find in central Seoul and unless you are super rich are often not in the best part of town. If you are there with a big company you may be offered a home in one of these.
The suburbs are also mostly highrises. Don't take anything on unless you have seen it in person. Arrange a hotel or something for when you arrive. The Koreans have a different world view, and often you can find you apartment block is next to an open sewer. There are still many open sewers there, and the stench in summer (aided by the extreme heat and humidity) can make it sickening to leave the house or open a window, so beware. Also they have huge problems with mosquitos and the like and you will find in the summer months vans spraying mossie pesticides randomly filling the streets with a fug. So you will need to find out when this happens in your are so you don't get caught out with the kids.
As I am sure you know it gets super cold in Korea in the winter. Seoul especially. Most places have underfloor heating. The reason I mention it is we were constantly getting caught out and stuff was getting ruined being left on the floor. chocolate, foods, well all kinds of things. When you do find a place if you rent it privately, then be VERY careful to bring a trusted speaker and reader of Hangul (Korean Language) who will help you through the twists of the contract, do not rely on what the estate agent tells you - or anyone who works for them - you must get someone independant to look at it BEFORE you sign, I know of loads of people who had big problems from signing things out of desperation to get into a home. Our apartment we discovered (and this was normal where we were) had its heating etc entirely controlled by the landlord. IN the winter - when it is super cold - he had it ramped up SO HIGH we had to open all the windows not to pass out. However much we begged him to turn it down he would smile and ignore us. There were loads of funny things int he contract that would have caught us out too and you must be careful. Will ask DH to remind me what they were when he is in from work.
There are loads of col stuff to do with kids, fun parks like Lotteworld are good. There is loads of culture to be seen the palaces and parks in Seoul are lovely. Seoul Tower, and if you want to tke a train trip to the suburbs there are gorgeous places like Suwon which is a fortified town with a palace to visit. In the winter they have big ice rinks in the city which are loads of fun.
The food is amazing. Korean BBQ obviously, loads of Japanese cuisine too as they were a japanese colony for a long time. All in all difficult when you first get there - but interesting and fun....