Is post office a proper noun?

The compound noun 'post office' is a common noun as a general word for a local branch of any postal service.

Examples:

I can stop at the post office.

The post office has shipping cartons.

The noun 'post office' is a proper noun as part of the name of a specific post office; for example, Springfield Post Office 19064 or Jackson Post Office 45640.

A proper noun is always capitalized.