"Post office" as a general concept is NOT a proper noun: It's a common noun, referring to any building where mail is processed and distributed.
However, "Post Office" can be a proper noun if it's referring to a specific organization:
* The United States Postal Service (USPS) is often referred to as "The Post Office". In this case, "Post Office" is acting as a proper noun, because it's the official, unique name of a specific entity.
* A particular branch of the USPS might also be referred to as "the post office" (with lowercase letters). This is still a proper noun, but it refers to a specific location rather than the entire organization.
Here are some examples:
* Proper noun: "I went to the Post Office to mail a letter." (Referring to the USPS)
* Proper noun: "The Post Office on Main Street is closed today." (Referring to a specific branch)
* Common noun: "I need to find a post office to buy stamps." (Referring to any post office)
So, the answer really depends on the context!