Actually there are lots to do in/near ICN. Depending on how much time you have, you can take a transit tour. They have 2 tours of 1 hr each (both free!) - one to a nearby Buddhist temple and another one to a shopping plaza I think. I took the temple one and they pick you up and drop you back to the airport in plenty of time (the tour itself is ok but a nice way to get out of the airport).

There are other tours you can get as well such as a longer tour that goes to the temple, a few other places and the beach. I think this one you can fit into the 6 hr slot you have. Longer tours would be for the day tour to Seoul etc. And the prices are all inclusive with food, transportation etc. The tour counter can even store your luggage (although I'd recommend leaving in the lounge under electronic lock if you can - will speed up re-entry into ICN secure areas upon return!)

You can find the transit tour desk right next to the Immigration desk and also after Customs on the arrival level.

Source: ICN layover last month