My favorite transit airport is definitely the Seoul/Incheon International Airport, which I almost always made connections when I visited my family in Manchurian China.
My transit time there usually last about 3-4 hours, in the afternoon, or in the early morning when the shops were mostly closed. Even during those wee hours, there were much comfort in that very considerate airport.
First, it was a modern facility with information clearly marked, at least in Korean and in English. There were also many labels and brochures with QR codes and there were QR code readers in the airport for travelers' convenience:

There was a Shuttle Train down below which will lead people from Incheon to Seoul:

People could also sign on for half-day tour of Seoul, to sample its cultural highlights, or Incheon, including its modern medical facility, to have a health check up or a botox injection done.
If stay in the airport, one could see the cultural/art gallery in the lounge area at any hour, or visit the Cultural Experience Center in the concourse level during business hours:

The lounge and hotel were in the Rest and Relax Area, which had many comforts, either one checked into hotel or not:
The Transit Hotel charged by 6 hours and cost about US$100 per shift:

The Lounge had many sections, open or more private, gave more economical travelers many options, from club lounge to comfortable chairs to sleep on:



It also offered free Internet and massage chairs and a screening room for news and movies:

A very convenient facility was the free shower during business hours, which had a large room with a cabinet, toilet, basin and a shower. A free towel was provided as well. I pushed my cart into the shower room and still was able to move able without bumping into anything:
Next to the Shower, there was Massage and Beauty shop:

In the same area, a Luggage Service and Library desk operated during business hours:

There were several cafeterias in the area, opened fairly early:

They also had a large Kids' Zone in the lounge area and a smoking room on the concourse level, for people had special needs:

Smoking Room
There were naturally many fancy shops, many of them had great store design:


If inclined, travelers could deposit them currencies to make donations to the Korean Red Cross. The container below I saw on the concourse held currencies issued from many countries:

All in all, it was a great airport with many human touches. It was also a very "green" one. For example, the escalators only operated when people were on it. The still escalators started very gently when people approached it and it would stop automatically when no one was using it.
When I was there, I always felt calm.
Label: Shenyang Trip 2012
