I have looked around a lot and I’m not sure what to try first. Someone had told me to just change the O2 sensor. But I’ve read that changing it won’t get rid of this code.

 

This code, P0420 is described as: "Catalyst system efficiency below threshold"
Basically it means the engine computer has determined there is a difference between your upstream and downstream 02 sensors that is out of range, it uses input from the two sensors (both mounted in the exhaust) to cross-compare and determine if your catalytic converter is working. The upstream sensor is used to determine the air/fuel ratio that the engine is running at and the downstream (post cat) is solely to confirm operation of the catalytic converter.

Reasons the code can come up:

• Failed Catalytic Converter (The honeycomb medium and its precious metal coatings can burn off and destroy the function of the cat. This is sometimes caused from unburnt fuel building up in the cat and burning)
• Failed Downstream 02 Sensor (These sensors see alot of abuse and do fail after ~75-100k miles)
• Major Exhaust Leak (This can let in atmospheric air and cause an improper reading from the sensor)
• Faulty Downstream 02 Sensor Wiring (Not super common but it can happen, shorts to power or ground and open circuits)

Troubleshooting:

• Does the car smell like rotten eggs? Or is there any unusual smells? A bad catalytic converter that is burning internally will have an odd smell.
• You can check over your wiring to see if you have any damage.
• You can use a multi-meter to check for continuity between your engine computer and the sensor
• You can use a multi-meter to check the resistance of the circuit within the sensor
• You can place a rag over the tailpipe with the engine running and listen for any exhaust leaks

Most shops see this code and just replace the sensor right off the bat, it's not always the solution, you are correct. Without troubleshooting with the steps I've listed your only real solutions are to first replace the sensor and then if that still reveals the code, then replace the catalytic converter. You could ask the shop to check for exhaust leaks and check all the wiring but they will still charge you $ and may not be honest, convincing you to still just replace parts.