Luzon.
One island off the coast of this larger island was the home of a nuclear waste facility at Dragon Gate, is located north of the Bashi channel, and is governed by Lanyu. In addition to Orchid Island, the Penghu archipelago is located to the west of this island. The Batanes Islands and the (*) Babuyan Islands are located south of this island, and this island's Ali Mountain contains sites called the Grand Sea of Clouds and the Flamboyant Cherry Blossom. This island's highest peak is at Yushan, and it is located north of the island of ?  Luzon. Separated from the mainland by the Strait of Formosa, for 10 points, identify this island whose capital is Taipei.
One island off the coast of this larger island was the home of a nuclear waste facility at Dragon Gate, is located north of the Bashi channel, and is governed by Lanyu.
{Taiwan} [accept {Formosa} early]