A Google Chromecast HD can be set up without using a mobile smartphone and without a computer
You do not need a mobile smartphone nor do you need a computer to set up a Google Chromecast. Rather, all you need is a display with a free HDMI input, a nearby free power outlet, and a Wi-Fi Internet connection. This video will show you how I set up my Google Chromecast with Google TV HD GA03131-CA (Canada). Interesting footnote: after factory resetting my Google Chromecast, the Chromecast's MAC address actually changed! (good to know if your home network uses MAC address filtering).