There are 3 Hilton Honors properties in Seoul:
http://www.flyertalk.com/forum/hilto...seoul-kor.html
http://www.flyertalk.com/forum/hilto...ilton-kor.html
http://www.flyertalk.com/forum/hilto...seoul-kor.html
If the OP wants to stick to the Hilton brand, I'd suggest browsing through those threads in the Hilton forum. There are tons of regulars over there who will contribute.
That said, on my last trip to Seoul, I stayed at the Conrad and would recommend it in a heartbeat. Was upgraded to exec room with a view of the river. The lounge and restaurant there were fantastic. It was a bit of a subway ride to get to some places, but I felt the property more than made up for that.
As for getting from ICN to the property, I just took the train to subway. On the return, I splurged and took the limo bus (had a bunch left on my T-money card, which works on that bus).
That said, I do speak Korean, so I was able to figure my way around rather easily.