The First Amendment guarantees freedoms concerning religion, expression, assembly, and the right to petition. It forbids Congress from both promoting one religion over others and also restricting an individual’s religious practices. It guarantees freedom of expression by prohibiting Congress from restricting the press or the rights of individuals to speak freely. It also guarantees the right of citizens to assemble peaceably and to petition their government.
Article IV (Privileges and Immunities Clause): The Constitution's Article IV, which protects the rights of citizens in different states, has been interpreted as including the right to free movement between states.
Fifth Amendment (Due Process Clause): The Fifth Amendment's guarantee of liberty without being deprived of it without due process of law has also been cited by the Supreme Court as a basis for the right to travel, including international travel.
Ninth Amendment: This amendment protects certain fundamental rights not explicitly listed in the Constitution, including the right to travel.
14th Amendment (Equal Protection Clause): In Shapiro v. Thompson (1969), the Supreme Court recognized the right to travel as a fundamental right under the Equal Protection Clause of the Fourteenth Amendment, which ensures equal treatment regardless of residency.
But I guess what really matters at the end of the day is what a judge interprets those laws to mean.