mosburger did a nice job summarizing some main points/thoughts so I thought I'd add a bit to them.

1. Vehicular traffic is definitely heavy. It'll be nice when they finish the airport train. I think I had good luck getting to and from the city when I went. I took a Limousine Bus which is basically a charter style bus that leaves the airport every 15-20 minutes or so on a set stop route. It returns the same way it goes. Various buses go to various stops. The Incheon Airport Website lists the most popular buses and their stops.
http://www.airport.or.kr/Eng/transportation/bus.jsp

2. Subway is extremely easy. Signs are also in English and station maps and area maps all over the place so you can find which numbered exit to take. Fare is by distance so you need to know which station you are going for the cost. Its inexpensive. Every subway station has a free and very clean bathroom too.

3. It seemed like English wasn't widely spoken, but I found a lot of signage to include English as well. Many restaurants have pictures that you can't point to for your dish. You can find someone who speaks English to help you if you are in a pinch. Food is reasonably priced.

4. Even though the subway is efficient and quick. It still takes time to get across the city. The historical sights in the Northern part of the city are fairly close together. Close enough it will be easier and quicker to take a taxi to get you right to the entrances of the sights. The two palaces I'd see on a limited time would be 1. Changdeokgung Palace (beautiful UNESCO pavilions & garden) 2. Gyeongbokgung Palace

Can't say anything about the ICN hotels as I didn't use them.