Watertown (or any other political subdivision of WI) may not have its own ordinances regarding GFSZ. Any licensee or oos licensee may carry with a license openly or concealed so long as they are not in or on the grounds of a 1-12 school.
Government buildings are off limits for anyone who is not a licensee. State Statute prohibits all persons including licensees from carrying in specific buildings or portions of buildings as you mentioned above. An airport may restrict or not restrict carry before a security checkpoint. Political subdivisions may restrict licensees from their buildings but not from their property. Political subdivisions may prohibit non-licensees from carrying on their property which includes parks, greenways, etc