Treaties become part of US law precisely because of the authority of the Constitution which allows it to be so. (US Constitution Article 6). If something is illegal under a signed treaty, it is thus constitutionally illegal, since constitutional provisions are specifically set out IN THE CONSTITUTION (US Constitution Article 6) which mandate that the treatises form part of the Supreme law of the land.

If you sign a treaty on torture it becomes Constitutionally binding, so you can't then say "oh wait, no, we're going to make legal provisions for torture", without that being unconstitutional, until such times as the treaties are amended through Constitutional process, which since the Treaty forms part of law, means that the signatories must agree to such amendments else the Treaty has been unconstitutionally defied. Guantanamo was not a Constitutionally processed entity: it was extralegal.

It doesn’t matter that the law is the law of the land as stipulated in the constitution. Breaking that law is not unconstitutional.

This is wrong. If the Constitution provisions through itself for Treaty to become Constitutionally binding, via guidelines in said Constitution, then breaking that Treaty without the due process required BY the Constitution to amend the Treaty, is by its very definition unconstitutional. When a law violates the constitution, it is an unconstitutional law. When a constitutional law is broken, that is a breach of the constitution. If Donald Trump bans Muslims from the US, and the Supreme Court decides it does not fit Constitutional law or the extensive body of Federal and Civil law forthcoming from it, then the ban is unconstitutional.

As for prisons, the purpose of a prison is to imprison, which must be carried out within Constitutional guidelines and within laws extensive to Constitutional authority. Reworking of these laws must be carried out through the Necessary and Proper Clause which demands that the Supreme Court and judicial bodies be given their Constitutional authorities on lawmaking and that laws be made through such proper channels. Judicial review is used to decide on the Constitutionality of entities, practices or laws, with the Supreme Court holding complete authority to arbitrate (US Constitution, Article 3, Section 1). It is not possible to modify the constitution or the laws of the land except through the means which the Constitution itself allows. Thus, if the Constitution mandates that all Treaties signed in accordance with the Constitution become Constitutionally binding (for instance, the UN Treaty on Human Rights), violating those treaties is a violation of Constitutional law as well as a violation of International law.

A lawful sanction is thus most definitely subject to the restrictions of signed Treaties which stipulate laws on torture and on what exemptions apply: they are the documents which govern the very legality of the thing, for goodness sake. If your government, having signed the Treaty in accordance with Constitutional provision, create a civil, military or federal law allowing for the torture of its citizens outside the legal definition of a "lawful sanction", which is the terminology used in the Treaty ( Black, Henry Campbell (1990). Black's Law Dictionary, 6th ed. St. Paul, MN.: West Publishing. p. 1341.), then it violates the Treaty, and it violates the Constitutional authority granted to that Treaty. It is not possible to create a "lawful sanction" which defies these guidelines. For instance, creating a law that says that it's okay to hold prisoners in small wire-mesh boxes in the cold for twenty-three hours a day with their arms chained behind their backs, does not meet the definition of "legal" sanction. It is an illegal sanction, because it cannot be justified in legal terms as a necessary degree of force either through the Constitution itself, the Federal framework, or through the Treaties to which the US Constitution grants supreme legality. Holding a prisoner in solitary confinement in conditions which meet the definition of acceptable sanction under the Treaty, would be a "lawful sanction". The only sanctions which can be "lawful", by definition, are those deemed lawful by the legally authoritative bodies of the Treaty authorized by and through the US Constitution.

US Reservations to the UN Convention on Torture:

(1) (a) That with reference to article 1, the United States understands that, in order to constitute torture, an act must be specifically intended to inflict severe physical or mental pain or suffering and that mental pain or suffering refers to prolonged mental harm caused by or resulting from (1) the intentional infliction or threatened infliction of severe physical pain or suffering; (2) the administration or application, or threatened administration or application, of mind altering substances or other procedures calculated to disrupt profoundly the senses or the personality; (3) the threat of imminent death; or (4) the threat that another person will imminently be subjected to death, severe physical pain or suffering, or the administration or application of mind altering substances or other procedures calculated to disrupt profoundly the senses or personality.

The practices at Guantanamo meet this definition.

(b) That the United States understands that the definition of torture in article 1 is intended to apply only to acts directed against persons in the offender's custody or physical control.

They meet this, also.

(c) That with reference to article 1 of the Convention, the United States understands that `sanctions' includes judicially-imposed sanctions and other enforcement actions authorized by United States law or by judicial interpretation of such law. Nonetheless, the United States understands that a State Party could not through its domestic sanctions defeat the object and purpose of the Convention to prohibit torture.

Which is exactly what George Bush did.

Also, from the Geneva Convention on Prisoners of War, Article 17:

Every prisoner of war, when questioned on the subject, is bound to give only his surname, first names and rank, date of birth, and army, regimental, personal or serial number, or failing this, equivalent information.

Prisoners at Guantanamo were physically and mentally tortured to give information beyond these.

No physical or mental torture, nor any other form of coercion, may be inflicted on prisoners of war to secure from them information of any kind whatever.

Whoops.

Prisoners of war who refuse to answer may not be threatened, insulted, or exposed to any unpleasant or disadvantageous treatment of any kind.

Whoops.

As for the compartmentalizations you propose: that the legality of the practices and conditions of Guantanamo can be separated from the prison's legality as a building, this is very unscrupulous: prisons are purposed to house prisoners, and the manner in which they are established and intended to be run ultimately decides their fitness for purpose. The prison at Guantanamo was purposed to exist in legally ambiguous space, institutionally engineered to allow and even to structurally encourage a form of imprisonment which is illegal and unconstitutional. Thus it is not fit for the legal purposes of a prison.

The man you began this argument with stated that Guantanamo is unconstitutional in that it detains prisoners in a fashion not concordant with Constitutional authority on the detention of prisoners. He is right: Guantanamo is not concordant with Constitutional (or international) authority on the detention of prisoners. Its practices and methods are entirely unconstitutional, internationally illegal, extralegal. At best the legality of the existence of the facility itself regardless of its purposes or methods -- in essence if it had no prisoners in it -- is legally ambiguous at best. Aside from the clear illegality of its methods, Bush placed this facility on a Naval Base in a country which the USA has no legal authority to hold civilian prisoners, with a government who do not grant the USA the right to carry out actions of war on its lands (of which detaining supposed POW's most definitely IS). Most damningly, the Sovereign nation of Cuba and its government confirm that they consider the presence of the US in Cuba as illegal under their own laws (as do the UN courts under the laws for the signing of treaties). As well as the fact that detainees, through entirely protected under the Geneva Conventions and UN treaties as per Constitutional authority vested in those agreements, were not granted Constitutional or international legal rights, which effectively means they were legally non-existent.

All of this is largely moot now, though, since the US Supreme Court in 2005 passed the Detainee Treatment Act, which, in summation, criminalizes many of these practices. In 2006, a ruling was also made that the legal positioning of the complex at Guantanamo had been specifically intended to violate through circumvention the principles of the Geneva Conventions and the Uniform Code of Military Justice. In 2008, Bush decided to push through Senate a bill that undid these rulings, which was, again, opposed by the Supreme Court, who ruled that not only was Guantanamo's legal positioning in regards to its purposes not "legal", but that it was in fact unconsitutional.

Guantanamo is a legal and constitutional fuck up, in every way conceivable.