Multiple outlets not working

I have 2 outlets that one in the bathroom and one in the bedroom that are closely together. The light in the bathroom and the light and fan in the bedroom has also stopped working. None of outlets are GFCI, the home was built in 1970. I've also went to the circuit breaker on the panel and checked that nothing has tripped. I tried testing the voltage of each circuit breaker on the panel outside of the house with a multi meter and they all read 120, so it's all good. I think the problem potentially started in the bathroom outlet when I plugged an appliance and it immediately just shut down. Any idea on how I can continue to troubleshoot?