Have done the deliberate <24 hr 'stop over' many times. best experiences are when there is a train servicing the airport and downtown.
SIN - a great place for this. Once had about 5 hours, so I caught the MRT from the airport to have dinner at 'Salt'; the restaurant tower had a station. Had dinner, returned to airport - all without getting out into the fresh air!
BKK - had about 15 hours, the highlight of which was to have dinner with drron and mrs.dr.ron
HKG - I asked for suggestions (see link in above post) and I did the Museum of Coastal defences and planned to do the cable car/Buddha, but weather was bad.
On recent trip to the Caucasus, I had <24 hr stopovers in Dubai (did the mall and tower things) Qatar and Abu Dhabi (planned to go and see the sights, but too bloody hot).
Note: Asian cities so much easier for <24hr quickie sightseeing than Gulf countries!!
When QF was flying into SFO, I used to get that flight then plan 6-8 hours before heading up to Canada. A sensational and easy place for a day goofing about.
HEL - hired a car and went down to Porvoo for a great seafood dinner with friends.
YVR - another good place for a short stop-over; catch the airport train to downtown or Yaletown and have dinner and/or walk along the waterfront.