If you are traveling within the United States only, makes sure to carry your original passport and visa document (i.e. Form I-20, Form DS-2019, Form I-797, Employment Authorization Card, etc.) If you are travelling far away from home or by bus, train, airplane. For local travel/close to home, simply carry pdf copies of above documentation on your cell phone.
Visiting Puerto Rico, US Virgin Islands or the Northern Mariana Islands: no valid visa is needed. You will need to bring your Form I-20 and an unexpired Form I-94, passport and visa.