The wizard school in the Harry Potter series is Hogwarts, formally Hogwarts School of Witchcraft and Wizardry. It is the central school for magical education in Britain and the main setting for much of Harry’s story.
Hogwarts is presented as a centuries-old boarding school located in the Scottish Highlands. Students typically begin at age eleven and study subjects such as Charms, Transfiguration, Potions, Defence Against the Dark Arts and Herbology. The school is divided into four houses—Gryffindor, Hufflepuff, Ravenclaw and Slytherin—each associated with one of its legendary founders.
According to the series’ history, Hogwarts was founded roughly a millennium ago by Godric Gryffindor, Helga Hufflepuff, Rowena Ravenclaw and Salazar Slytherin. Their disagreement over admitting Muggle-born students eventually helped create the school’s central ideological conflict.
Ilvermorny is another wizarding school, but it is located in North America. Durmstrang and Beauxbatons are European schools that appear in the wider wizarding world, especially during the Triwizard Tournament. They are not alternatives to Hogwarts in the question’s British setting.