Easy - You insulate where there would be an ADVERSE effect with regards to temperature if you DIDN'T insulate the wall (or floor or celing, for that matter.)
If you want to heat one room and cool another room that's butt-up against it, then insulate. If the rooms are to be ALWAYS at the same temperature, don't insulate the wall.
My best to ya and hope this helps.
Jay J -Moderator
PS: If you want to spend that $$$, then consider sound-proofing material. THAT might prove useful ...
PPS: God Bless America!
However, for sound insulation purposes, insulation in all walls is worthwhile. It is relatively cheap compared to other building expenses and you will thank yourself for insulating your bedroom or den from your kids room when they are teenagers!