Wi-Fi rules the world
Just as you use it at home to avoid wasting your monthly data to stream episodes of Brooklyn Nine-Nine, Wi-Fi allows you full access to the web and apps without tapping into even a moment of international roaming. Major brands of smartphone even allow you to operate in Airplane Mode with the wifi still ON -- guaranteeing full internet usage without the danger of data charges.
Rent a burner
Why risk taking your expensive iPhone 6s abroad to get pinched by pickpockets when you can rent a temporary one instead? Outfits like Cellhire USA, Cellular Abroad, and Telestial offer temporary calling plans and current phones (no Motorola Krzrs here) specifically for overseas use, usually for a preset fee much lower than it would cost to bring your own device. Whichever service you choose, though, make sure you ask the right questions to pinpoint if the temp phone fits your needs. Does the plan include unlimited minutes, data, and text? Does the service support incoming and outgoing calls inside and outside of the host country? If you cross over into another foreign country from the nation you originally visited, does the service travel with you? Make a list of such questions and follow through until all of you concerns are squared away.
Also, and most important: lock up a temporary phone before you leave rather than picking one up when you arrive. The domestic offering is usually much cheaper.