Basically, one is not forced to travel to any other state. Unless you are required to, by law travel to another state, ALL travel is voluntary. The fact that you may need to go, on business, or for any other personal reason is a matter of personal choice.
No, there is a right to travel freely from state to state at will and nowhere is it written in the constitution that one must leave fundamental civil rights behind.
Imagine a state law that forbade entering NY with a Bible or a Koran. Imagine a state law that said the 4th amendment didn't apply in NY for out of state residents. Or a state law that said you could be traffic stopped without RS or PC, because you have an out of state license plate.
None of these scenarios would survive ANY judicial standard of review, and neither should the denial of second amendment rights.