The storage path for logs, created over Chia GUI is different depending on your OS. In Windows you can find the Logs under C:\Users\%USER_NAME%\.chia\mainnet\plotter.
If you create your plots via CLI, then you see the output in your terminal. To store that output in a file, you could use stream redirects.
For Windows users - I made a plotting PowerShell script, which simplifies planning of plotting queues, displays the progress in terminal and at the same time stores the output to the log folder.