What do you do with the water heater when you shut off the house water?

Nothing. If you will be gone for long time, turn off the gas or electricity. Even with street water off, there is still pressure. If you will be opening a line, drain the pressure by opening a faucet.

If you are only going away for a week or two (or even a month), I'd set the gas valve thermostat to PILOT or VACATION SETTING. In this way, when you return you can simply turn the thermostat back to its original setting without having to relight that pilot!

Mark