How do I locate transferred files after using Migration Assistant on iMac?

I used Migration Assistant to transfer data to a replacement computer via an external drive. The old computer has failed so it could not be included in the process. I unchecked programs because I intended to upgrade these anyway so I chose just to transfer files and documents. The process proceeded as expected, taking quite a while, and an on-screen message confirmed success. Problem: I can't find the files anywhere. Advice please.

[Re-Titled by Moderator]