If you wish to travel outside the U.S. and re-enter during your approved appointment period, you should be sure to have the following things at the time you re-enter the U.S.:
If you have an approved permanent resident petition (I-140) filed by NYU and will be re-entering the U.S. in H-1B status, you should also carry a copy of your I-140 Immigrant Petition approval notice (Form I-797). Further, if you have applied to the USCIS for adjustment of status (I-485), you should also carry the USCIS receipt showing submission of your adjustment application.
If you are traveling with your dependents, make sure that you carry all items listed above, and that they possess a valid passport with valid H-4 visa stamp for re-entry. If they need an H-4 visa, they must also present to a U.S. consular official proof of relationship to you (i.e., a marriage or birth certificate), documentation showing financial support (this can be a brief letter from you if you intend to support them on your salary along with copy of your employment letter), and your original I-797 approval notice for H-1B status (or their original I-797 showing proof of H-4 status if they ever obtained one). If they are applying for an H-4 visa independent of you and do not have their own original I-797 approval notice for H-4 status, they should submit a photocopy of your I-797 H-1B approval notice.
Most H-1B scholars do not need a new U.S. visa to return to the U.S. after visiting Canada or Mexico due to a process known as Automatic Revalidation. If you travel to Canada or Mexico, for 30 days or less, you do not need a new visa stamp even if your current one has expired if you:
Automatic revalidation of visa does NOT apply if the scholar:
Note: Citizens of some countries may need a visa to enter Canada or Mexico. Please check to see if citizens of your home country are required to have a visa stamp (e.g. a Canadian tourist visa) to enter an adjacent country.
When the immigration inspector notes your I-94 information upon re-entry into the U.S., be sure to check at that time that it is noted with the correct visa status in which you are intending to enter the U.S. (If, for example, you are an H-1B professor and the immigration inspector notes "B-2" on your I-94, you will not be eligible to work!)