You have the right to travel freely within the U.S. provided you maintain your legal J-1 status. Carry your passport and immigration documents with you when you travel.
The rules differ based on whether you are returning to the same program sponsor or a different program sponsor.
J-1 scholars and J-2 dependents are required to have valid travel signatures on their DS-2019 forms when returning to the U.S. to continue their J-1 programs.
An I-94 is an arrival and departure record that is issued by a Customs and Border Protection (CBP) officer, in either paper or electronic format, to foreign visitors entering the U.S.
J-1 scholars whose visa has expired may be able to return to the U.S. after traveling to Mexico, Canada and neighboring islands/U.S. territories under certain conditions.