I'm traveling to Hong Kong and I want to install an app on my iPhone which will allow me to text for free to non-smart phones in Hong Kong (specifically, to this provider: +852-90207 XXX). Is there any app or service that would allow me to do this?
Regular texting costs money. Not a single company in the world will offer you unlimited texting across nations, simply because they have to make costs as well.
There are plenty of alternatives to text for free between smartphones (iMessages, WhatsApp, FacebookChat, BiteSMS, Text Free,...) but you'll need a Smartphone and a internet connection.
But I'm sure if you can afford yourselve an iPhone, you won't die of starving when paying for a 10c text to Hong-Kong ;-)