Keeping USCIS informed of your address is critically important. Not only is it actually required for most aliens (see INA §265), most people are unaware that there are criminal penalties for failing to report a change of address. See INA §266. While violations are rarely enforced, the consequences of failing to update your address with USCIS can have disastrous consequences. It is not uncommon these days for USCIS to issue a Request for Evidence (RFE) while adjudicating a case. Sometimes these RFEs can come many months, if not years, after a case is filed. If, however, you moved from New Jersey to New York during the pendency of the case and did not change your address with immigration, you may not receive the RFE and, consequently, the case might end up getting denied.
Changes of addresses are performed by completing the Form AR-11. One can also call the USCIS customer service phone number at 1-800-375-5283.