Why did Sirius have to travel north in GOF?

In "Harry Potter and the Goblet of Fire," Sirius Black is on the run and hiding from the Ministry of Magic, which believes him to be a murderer. He travels to meet Harry in a cave outside Hogsmeade, a location near Hogwarts, to provide support and information to Harry during his participation in the Triwizard Tournament12. There is no specific mention of Sirius traveling north for a particular reason other than to meet Harry and provide guidance. However, his general movements are dictated by his need to avoid capture and maintain secrecy while supporting Harry from afar.