The hotel limo bus was pretty easy for me when I was there to/from the airport. Although the Conrad is the 2nd stop out of the airport and the second to last pickup before getting there, so I did not have to sit through many stops. It is like $15 US each way and was not crowded at all on July 1 when I was there.
The people there told me which one to buy a ticket for and where to wait for the bus. it is really straightforward. I did not take a taxi at all, I got a T-Money card and public transported along with much walking.
For a shopping plus tower experience, Lotte World and Lotte Tower was cool. It was cloudy and raining when I went, but the view should be pretty good if you can see the city.