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Do qiskit simulators run locally or on IBM cloud servers? It seems that each time I have used them, my computer goes into max CPU, and sometimes the simulation runs out of memory, exiting with out of memory error message.

habercde
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creet
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Both, depending on the backend that you choose. If you install and run Aer, then the simulation is local. But you can also run a simulator via IBMQ, as if it was a real device. There are several simulator backends on the cloud, like ibm_qasm_simulator. They are listed at the bottom of the webpage https://quantum-computing.ibm.com/services?systems=yours.