The one spot I have gone to quickly see a city during a layover is Singapore. However, they make it easy for you
Another good one is Amsterdam. Train station right in the airport takes you right to the city center in about 15 min. They actively promote it if you have a four or so hour layover or longer. First time I visited we had seven hours, we actually took the train into town, rented bikes for three hours for 10EUR-ish, and saw quite a bit of the sights (and by sights, I mostly mean the brewery in a windmill) that way.