My husband and I are in a constant argument about turning down the water
Heater while we are on vacation for only one week. If no one is in the house
And using the water... what is the point?

It depends on how long you are gone, how big it is, and how well insulated it is, variables not easy to measure all combined. Returning home means heating up a whole tank again. In general I would say that it is worth turning down a 40 or 50 gallon one if you are gone a week and turning it off if more than a week. I turn my down for the summer and up for the winter, and make sure it's never set so that the hot water ONLY is too hot, AND that the shower doesn't run out. I think that's the most savings on a day to day basis. It takes a little juggling twice a year.
I'm not a plumber so the excellent plumbers here might disagree or have more to say.

Turn it to "Pilot" if it's gas and turn off breaker if it's electric and save money.