The claim that the sitting US President isn’t supposed to declare war on US cities is mostly true because the US Constitution grants Congress the sole power to declare war, and there is no legal authority for a president to declare war on domestic locations; however, the president does have certain war powers related to national defense and military deployment under specific conditions.
The sitting US President isn’t supposed to declare war on our own cities

Presidential Power In War And Peace - Hoover Institution Presidential Power In War And Peace
Source: hoover.org
Key Evidence
The Constitution grants Congress exclusive authority to declare war.
quora.comquora.comWhere in the US Constitution does it say the president cannot declare war?
The War Powers Resolution restricts unilateral presidential military action.
en.wikipedia.orgen.wikipedia.orgWar Powers Resolution
Presidential powers include directing defense-related actions but not declaring war domestically.
law.cornell.edulaw.cornell.edu47 U.S. Code § 606 - War powers of President
reddit.comreddit.comr/Presidents on Reddit: can a President declare war through executive order?
Political reactions condemn any suggestion of military action against US cities as improper.
foxnews.comfoxnews.comDemocrats slam Trump for 'war' threats targeting US cities: 'Not your war zone'
What the Evidence Shows
The US Constitution explicitly assigns the power to declare war to Congress (Article I, Section 8), not the President.quora.comquora.comWhere in the US Constitution does it say the president cannot declare war? The President, as Commander in Chief, can direct military operations but cannot unilaterally declare war. The War Powers Resolution of 1973 further limits presidential authority by requiring congressional approval for extended military engagements.
en.wikipedia.orgen.wikipedia.orgWar Powers Resolution
While the President has some authority to act in defense of national security, including directing communications or deploying troops temporarily, these powers do not extend to declaring war on American cities or domestic territories. Such an action would conflict with constitutional protections and legal norms. The political controversy referenced in highlights that threats or rhetoric about using military force against US cities are widely criticized and seen as inappropriate or unlawful.law.cornell.edulaw.cornell.edu47 U.S. Code § 606 - War powers of President
foxnews.comfoxnews.comDemocrats slam Trump for 'war' threats targeting US cities: 'Not your war zone'+1 more
Therefore, while the President has significant military authority, declaring war on US cities is beyond constitutional and legal limits.