Note: Some commercial services on the internet provide information that is so frequently erroneous or incomplete as to rise to the level of malpractice -- sometimes even to the level of fraud. Which is why I cite statutes and case law to support my answers, so you can verify them independently. Caveat Emptor.
NY CLPR 5222 describes the law concerning enforcement of judgments against a debtor for any personal property other than the debtor's wages
held by an employer (which is restrained by "garnishment," which is a separate legal process). A restraining order has a one-year lifespan, so if one has been issued against you at any banking institution, then you may as well forget about that bank for the next 365 days.
If the judgment was issued by a NY court (other than a U.S. District Court), then it is only enforceable in NY, unless the judgment is separately registered in a different state jurisdiction. Because of this, a debtor can open a bank account in another state, at a state-chartered bank with no branches in NY, and effectively avoid all attempts to execute against the debtor's accounts, unless and until the judgment is registered in the new state jurisdiction.
And, because it is practically impossible for a creditor to determine where a debtor banks (due to federal banking privacy laws), except via a judgment debtor examination, by using a bank in a different jurisdiction, the debtor can play "cat and mouse" at least 50 times (50 states and D.C., plus Virgin Islands, Puerto Rico, Guam, American Samoa). No creditor is so diligent as to follow the debtor to every state. Though, it's quite inconvenient to have to worry about moving money around.
Re the homestead exemption, it is:
- $150,000 for NYC counties, Suffolk, Nassau, Putnam, Rockland, and Westchester counties,
- $125,000 for Albany, Columbia, Dutchess, Orange, Saratoga, and Ulster counties, and
- $75,000 for all other counties
NY CLPR 5206(a).
Hope this helps.