Regarding Internet and Wifi, Greenland is not quite as good as the rest of the Nordic countries.
Many hotels offer Wi-Fi hotspots or in-room internet access, though the usage costs may be higher than what you’re used to in other countries.
Please note that the internet in Greenland tends to be slow since it is a satellite connection.
When travelling in Greenland, you will also find the opportunity to check your email at the nearest tourist office in larger towns.