i/O or Logic Board?

It depends on your knowledge level and skills!

Some people use the swap out method having spares of some of the parts. Over time you tend to learn what is the more likely part to fail and have as spares.

Others use a digital Ohm/Volt/Amp meter to troubleshoot the logic using schematics and board views. But you need to have a good understanding of analog and diagonal electronics.

I try to use a logical approach to isolate the issue based on how the given system is setup. As an example your MacBook Air logic is broken into two parts the main logic board and the I/O board so assuming you have power in the battery what is not working? Is the headphone jack has failed then its most likely the jack or the cable which passes the signal to the I/O board. So I might replace the cable if it looked ratty or replace the I/O board if I see any corrosion on it.