Kevin avoiding the police

We get it, if Kevin went straight to the police there would be no movie. He was p/o'd at the family and wanted to enjoy a vacation without them. He also wouldn't have brought justice against Harry & Marv and saved the charity money. But after the fun and work was done... why doesn't he go straight to a police station and tell them he's lost and his parents are in Miami? Would he have just spent the night at Rockefeller Center and then wandered NYC forever until his parents came to find him? You would imagine after the first time this happened, his parents would have instructed him to go to the police so they can be reunited.