Which areas do I remove copper pour to reduce noise?
You don't remove copper pour to reduce noise. An unconnected copper pour will have more noise than no copper pour, but having a grounded copper pour tends to reduce noise or at least keep it the same compared to no copper pour.

You remove copper pour to get rid of parasitic capacitance for sensitive circuits like oscillators an RF, and leakage currents for really high impedance circuits which operate on miniscule currents. And even then, it's not a universal rule since the right copper connected to ground can help things in instances with leakage currents.

If you're that worried about EMI, you should be using a 4-layer board with a ground plane.