There are several sites that aid in associating a bank with its routing number.

Bank routing numbers organized by state are here, on a private investigator’s web site. Search The Federal Reserve Bank, FedWire participating financial institutions by name, state or complete, or partial, routing number. A private company, has a free bank routing number search tool. [Brought to my attention by Jim Magdaleno.]

Once you know the name of the financial institution, go to the Federal Reserve site to identify the bank’s location.