Nachos - I think you've gotten a response about the Airport bus but not on the subways. Yes, in my experience as a non-Korean speaker the Seoul subway system is easy to navigate - signage is in both Korean and English. The lines are color-coded, and each station has numbered exits and signs direct you from platform to the right exits. You'll notice that guidebooks tell you which exit to use by number.

That said, the stations are sprawling, multi-level shopping arcades and there can be a lot of stairs and walking - it may be a block or two (or more) walking underground to get to the exit you need. Like any big city the stations can be very crowded if you and your wife are also pulling suitcases or carrying bags.

To and From the airport I'd recommend using the airport limousine bus that stops closest to the hotel, but for sightseeing and getting around I'd recommend the subway. Buy a prepaid T-Money card at a convenience store at the airport and load it with cash for your stay - you can use it on the airport bus, subway, and most taxis.