Going out of town for a few months and having the water shut off. Do I need to drain my water heater ?

No. Turn the gas or electric off to the tank too.

In addition to the abobve advice: Gas water heaters have "Vacation" thermostat setting. Or as suggested above, shut off incoming gas to the water heater completely. You can flip OFF breaker supplying elec. Heater. Hope that helps. Milo