Final answer:
The sentence should use commas to separate the names in the first list and semicolons to separate the city and state pairs in the second list to avoid confusion and maintain clarity.
Step-by-step explanation:
The correct punctuation for the sentence 'Cora, Emily, and Elliot visited relatives in Boston, Massachusetts; Durham, New Hampshire; and Portland, Maine.' would be to use both commas and semicolons. Commas are used to separate the names in the first list (Cora, Emily, and Elliot), while semicolons are used to separate the items in the second list that already include commas due to the pairing of city and state (Boston, Massachusetts; Durham, New Hampshire; and Portland, Maine).
The use of semicolons is crucial in the second list to avoid confusion, as each location consists of two parts that are separated by a comma. Thus, the semicolon acts as the separator of larger list items that already contain commas, which presents a clear and concise enumeration of the places visited. In contrast, the names in the first list do not have internal commas; thus, only commas are necessary.