I have an I-130 petition approved, can I travel within the US with my approval notice?

Approval of a Form I-130 Petition for Relative Alien does not, by itself, create any nonimmigrant or immigrant status. That is the first step in applying for adjustment of status (if already in the U.S. and otherwise eligible) or consular processing (if outside the U.S. and otherwise eligible) based upon approval of the Form I-130. There is a backlog for visa availability for many family-based adjustment of status cases, so in order to determine whether you now are eligible to file for adjustment of status, it would be necessary to know more about your circumstances, including the family relationship specified in the Form I-130. If you already are in the U.S., you will need some other valid visa in order to be lawfully present. Be aware that in order to apply to adjust status, one must be in valid nonimmigrant status in the U.S. Also be aware that in most instances if an adult is unlawfully present for 180 days or longer, he/she will be subject to a 3-year bar to re-entering the U.S. (if unlawfully present, the bar may be a very harsh 10-year period). If you are now outside the U.S., you will need a valid visa to enter and travel within the U.S. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.