Actually there is no "right to travel". Where would you get the idea there is such a thing?
Yes...there is a right to travel. It's a firmly established constitutional doctrine.
This is why I love people who argue on forum boards without legal degrees. It's funny.
US Constitution Annotated - The Right to Travel
The Right to Travel
The doctrine of the "right to travel" actually encompasses three separate rights, of which two have been notable for the uncertainty of their textual support. The first is the right of a citizen to move freely between states, a right venerable for its longevity, but still lacking a clear doctrinal basis.1858 The second, expressly addressed by the first sentence of Article IV, provides a citizen of one State who is temporarily visiting another state the "Privileges and Immunities" of a citizen of the latter state.1859 The third is the right of a new arrival to a state, who establishes citizenship in that state, to enjoy the same rights and benefits as other state citizens. This right is most often invoked in challenges to durational residency requirements, which require that persons reside in a state for a specified period of time before taking advantage of the benefits of that state's citizenship.
Thanks for playing.

Don't let the parts about the uncertainty fool you...this gets actual use all the time when combined with the full faith and credit clause so that when you move to a new state you dont get discriminated against.
The premises they use are about laughable
The Constitution does not contain the word "travel" in any context, or even a mention of any explicit right to travel
The constitution references many freedoms and there are indeed laws that lay out freedoms specifically.... but again, just because something is a freedom, law, or privilege does not make it an inherent right
The right to "locomotion" (I.E. walking, crawling, etc under your own power) as it is sometimes called, has been attempted to be used to define a 'right to travel' in many cases including cases of driving without a license... and this is mainly unsuccessful because there is not constitutional right to travel