Before you go, load up on apps that can be used offline or without data. I downloaded PocketEarth, an offline maps app, so that I could access maps even when I didn't have Wi-Fi. (In London, I used the Google Maps app, which didn't require very much data.) I also downloaded WhatsApp so I could text over Wi-Fi (with contacts who also have WhatsApp).
See which apps are popular in your destination. I use the taxi-hailing app Hailo all the time to get cabs in Boston, so I was surprised to see how ubiquitous it also was in London. Be aware that your app accounts may be linked to your phone number, so you might have to reregister if you are swapping SIM cards.