Right now, Icelandair will set up its customers with a buddy to show them around on their visits. Now KLM Royal Dutch Airlines, the Dutch carrier, is jumping in on the "local guide" trend.
If you're connecting through Schiphol Airport on KLM—and some 70% of its passengers do—then you qualify for a free local guide as long as your layover is for six hours or more. The airline will give you a free train ticket from the airport to the center of town, and clear directions for finding your buddy, who will be selected for based on the things you want to see. They'll treat you to a free drink (if you want one) and then show you the town.
KLM's program is a little harder to use than Icelandair's. That's because participants must have an iOS (Apple) mobile phone and be able to make calls or text, or at the very least Wi-Fi. That's so the local can reach you and because once the meeting is over, a free app comes up with a schedule to make sure you get back to the airport in time. The program runs March 22 to May 31, and it's only for customers who originate their trips in North America or Italy.
Finally—a reason to want to make you layover longer.
KLM's information page for "Layover with a Local" is here: https://layoverwithalocal.klm.com.