Careful with the breaker test: do not switch off the main if you're not sure which breaker is which, and don't touch the meter itself. But yes, if you can safely turn off everything in your panel, the little horizontal wheel or digital pulse on the meter should basically stop. If it's still moving fast, something outside your apartment is on your circuit.
@firstwinter: The oil-filled radiator is not 'cheaper' in terms of electricity. It's still a 1500W resistance heater. The advantage is it releases heat more slowly, so the room doesn't swing as much. If that allows you to keep the baseboard off or at a lower setting, you may save. If you're running both, you're paying more. There's no free heat in an electric apartment—every dollar of warmth shows up as kWh.
@EastHarlem_E: A 5 a.m. spike is a red flag. In a prewar building, the boiler circulator, hall lights, or a roof exhaust fan sometimes get tied to a tenant meter because it was easier when the wiring was updated. Write down the meter reading at night, turn off your own breakers if you can, and check again in the morning. If the meter moved with your panel off, call Con Ed and ask for a meter investigation. They won't always admit a wiring fault, but they can send someone to check if the meter is feeding only your unit. Also, don't touch any junction box or open panels—just read the meter.
For your specific bill: $210 in a cold month with electric baseboard in an old place is not automatically a mistake, especially if the apartment was vacant before and the previous tenant had heat at 75. But the delivery charge is real. Con Ed rates have been climbing, and delivery is often more than supply. The only permanent fix is to get off electric resistance heat, which you can't do as a renter. The best smaller fix is to close off rooms, use a small fan to push warm air around, and make sure you're not heating the fire escape.