More than a decade ago, when I was still traveling alone between EU and the DR, I had a few very nice experiences in the winter time going through JFK as missed connecting flight to MIA and had to spend a night on a metallic bench near toilets at the airport... I was young, I had no money nor knowledge of any hotels etc, just wanted to get on my flight quickly...
However, all this was fine, the worst experience has been definitely on a direct flight FRA-POP (almost 10 hour flight as such), with the kids being small a few years ago, we were already on the final approach coming to POP (we were about over Costa Dorada but could not see it from the clouds), when the plane started climbing suddenly and the captain let us know that we cannot land to POP due to weather, we're going to PUJ instead... Then with charter buses from PUJ to POP and there was no circunvalacion yet in the capital, so we actually had to go through it... Travel time, carrying our youngest was about 24 hours on that trip, including a few hours at PUJ airport waiting for passport control, then luggage, then transport...