If you have direct spark ignition, then turn the water heater on first thing in the morning until it shuts down. Then turn it off. That will leave you with hot tending towards warm water for most of the day.
If you are planning on a shower, then turn it on before you shower.
My ten gallon unit cycles every 4 hours and runs for 15 minutes. Why exactly would I want extremely hot water at say 3 am?
And propane is NOT cheap.
If you are at a campground which includes electricity as part of the pad fee--by all means leave the water heater on.