Is there a way to find out when and where money sent from a U.S. bank was credited to my bank account?

If your US client sent you money, it is most likely they used Society for Worldwide Interbank Financial Telecommunication (SWIFT) (SWIFT) to transfer the money. Please ask them to provide you a SWIFT MT-103 message format. This will allow you to know exactly where the wire is (it is usually used to trace the wire).