You do not need special papers to travel from state to state or to U.S. territories but you must always carry your immigration documents. This is particularly true while traveling through states along the Mexico or Canada borders. You could be stopped by immigration officers at any time and told to produce the following:
Valid, unexpired passport (expiration date at least six months into the future)
Valid, unexpired I-20
U.S. visa (expired or unexpired, unless you are a participant in the Visa Waiver Program)
Employment Authorization Document (EAD) card and employment verification documents if you are on Optional Practical Training (OPT), the 17-Month OPT Extension, and H-1B Cap Gap Relief.
Non-contiguous US States and Territories
If you are already legally in the U.S., you do not need a visa to visit Hawaii, Alaska, Puerto Rico or U.S. Virgin Islands unless your travel plans include entry to another country en route to these destinations. You will need to take your valid, unexpired I-20 and your valid unexpired passport.