https://www.aclu.org/other/constitution-100-mile-border-zone
I think it’s generally well established that rights travel abroad with citizens. However, it’s less clear if they apply abroad (or even to U.S. territories) to non-citizens. E.g. United States v. Verdugo-Urquidez claims it does not apply to non-citizens who do not have a voluntary association with the U.S.
Edit: I'll try to be more clear. The rights of U.S. citizens extend beyond the border when dealing with the U.S. government. I was not implying other governments must recognize U.S. Constitutional rights when dealing with U.S. citizens.
I would be incredibly surprised if that argument held up.
https://www.aclu.org/cases/al-aulaqi-v-obama-constitutional-...
https://www.aclu.org/cases/al-aulaqi-v-panetta-constitutiona...
There are also questions about scenarios like https://en.wikipedia.org/wiki/Anwar_al-Awlaki, where a US citizen was executed by the US without trial while overseas.