I would say to go straight into the city. Check in to a hotel perhaps near the center of the city (see Luxury Hotel thread for hotel ideas such as Westin Chosun, Plaza, Lotte etc.). Then you have a bit of time to explore the city. Maybe you can get a good Korean dinner before retiring for the evening? Korea House Royal Cuisine might be one option. If you have time after dinner, why not check out Myeong-Dong Night Market area. Youtube video of Myeong-Dong. Or Cheonggyecheon Stream. Cheonggyecheon Stream is a nice place to visit.

Hotels near the airport are good but boring. You can get a better feel for Seoul just coming into the city. If you take the Airport Express train, the Seoul stop is many levels below ground. It might feel like you have to take multiple escalators and/or elevators to finally get to the ground level. The entrance/exit to the Airport Express is near the Rear entrance to Seoul Station. Taking a taxi from there to your hotel might be a good option. The other option is to take the escalator up to the main floor of Seoul station, walk all the way across and then head down from the main entrance of Seoul station where there is usually a line of taxis outside. Or if you feel really adventurous then jump onto the subway and make your way to your hotel!

January tends to get a bit cold so be prepared.

Also regarding the City Airport Terminal, it seems they only handle check in and immigration if you are flying Asiana, Korean and Jeju Air.

Have fun, let us know how things turned out for you.