Wade Academy was the place all the school children in Stain'd-By-The-Sea were transferred to in Shouldn't You Be In School? after Stain'd Secondary burned down by the villain in this series, known as Hangfire. Hangfire was planning to kill or torture the children in Wade Academy in some way.
Wade Academy is located on Offshore Island which, due to the draining of the sea, was then just a cluster of rocks. A bridge came out of Offshore Island but it was no longer needed after the draining. By Offshore Island was the Clusterous Forest, a forest of seaweed that mysteriously survived the draining.
In Shouldn't You Be In School? Stew Mitchum was the guard in the hallways of the Academy. When Lemony Snicket arrived, Stew knocked him unconcious and Ellington Feint, Lemony's possible love interest, came and saved him with some coffee and a wet cloth. She explained to him the dangers of the school and why he shouldn't have been there.