I have a Sony boom box with cassette tape , I wish to transfer old tapes to CD;s I have a headphone connect on the boom box - but where do I connect at my computer ( microphone or headphones with an audio to audio cable ??

The boom box should be connected with an appropriate audio cable to the “Line In” of your computer.
Note that many laptop computers do not have a “line in” connection.
In some cases laptop computers have a combined “line in” and “mic in” socket, so it may work plugged into the “mic in”.

A “mic in” is not really suitable (unless it is a combined “line in” and “mic in”) because it is designed for a really low level, mono microphone signal and not for a high level stereo signal.

If your computer only has a “mic” input, then the correct solution is to get a sound card that has “stereo, line level” input. The Behringer UCA-202 is a cheap USB sound card that has stereo line inputs and outputs (about $30).

The “headphone” socket on the computer is an “output” (sound comes out of it) so it cannot be used as a recording “input”.