Personally, I am biased towards ICN because I did a lay-over there for 13 hours and got about 8 hours of good sight seeing. Simply take an airport bus to the city hall which takes about 45 minutes and costs about $7 and you have a great launching point to see some of the palaces and grab a good lunch. One thing that I wasted about 2 hours on was trying to find a bus back to the airport and taking the train to Gimpo and a bus from there. If you can avoid this pit fall, you can easily get a meaningful day in Seoul and get to see a city that is often overlooked on trips to Asia. Otherwise, I would suggest Tokyo as a separate visit and would suggest avoiding Nagoya because it seems like it's too spread out for quick sight seeing. Also, if you arrive in Singapore well rested you can easily get to see a number of sights in 7 hours if you take a taxi from the airport.