Morgan's Point is located 30 miles southeast of Houston in southeastern Harris County, Texas, United States, located on the shores of Galves…Morgan's Point is located 30 miles southeast of Houston in southeastern Harris County, Texas, United States, located on the shores of Galveston Bay at the inlet to the Houston Ship Channel, near La Porte and Baytown. As of the 2020 census, it has 273 residents, and is located within the La Porte Independent School District.