The Isle of Thizzian is a rocky island with a single, tall, and narrow mountain spire. There are sea stacks around the island. Vegetation consists of grass, trees, and the Sassafras plant.
This island may be located not too far from Dragon's Edge, as Hiccup indicates that he and Astrid are "only gonna be gone for a day or two." This time would include travel both ways, as well as staying on the island and harvesting sassafras.
In "Dawn of Destruction", Hiccup and Astrid go to the Isle of Thizzian in search of Sassafras Albidum plants, which grow only on this island. They spend some alone time together and go in a moonlit flight, then go back to the Edge.