I have never thought about finding all of the places named for Christopher Columbus, but there are certainly many such places. In the United States alone there are more than 30 states that have a city named Columbus.  When we think of Columbus, though, it is most common that we think about Columbus, Ohio, the home of Ohio State University. 

Also, the capital city of the United States, Washington, District of Columbia, is named in honor of Christopher Columbus. Other places with the name Columbia also are named to honor the explorer. Columbia is the capital of South Carolina and there are many other Columbia's throughout the United States. Some of these states include Maryland, Washington, and Missouri. Additionally, many states throughout the United States have Columbia counties.

In Canada, the province British Columbia is named for him.

Throughout other parts of the world there are many references to his name. The country Colombia in South America is named for him as he explored much of the surrounding area. Cities named Colon are also a reference to him as his name in Spanish is Cristobal Colon. 

Many different places in the world have been named for him and though we don't always think about all of these places, when you see the alternate spellings that seemed to have derived from his name such as Columbia, Columbus, Colombo, Colon, there is a good chance they too are named in honor of Christopher Columbus.