Allison and Michael Busam recently took their three daughters, ages 11, 9 and 7, to a school fair near their home in Summit, N.J., where they found a teacher they knew sitting on the bench in a dunking booth. He was promptly dunked three times. The soggy teacher told the Busams he was attending his reunion at Summit High School that night. Since moving to Summit from Hoboken 10 years ago, the Busams hear stories like that all the time. “I know a million people here who grew up here,” Ms. Busam said. Summit, a city of around 21,000 with...