Mystery in the Sand — Gertrude Chandler Warner

One warm night four children stood in front of a bakery. No one knew them. No one knew where they had come from.

Henry, Jessie, Violet, and Benny used to live alone in a boxcar. Now they have a home with their grandfather and are spending the summer living in a mobile home on the beach.

One morning Benny finds a valuable gold locket in the sand and decides to try to find its owner. Soon, the Boxcar Children are caught up in a puzzle that involves shadowy figures on the beach at midnight and the mysterious Miss Smith who seems to live alone in the big Tower House nearby....