The only time I leave without a full water tank is when I need to leave with the trailer winterized. In that case I fill the tank at a gas station when I get out of the freeze zone. I have never had a problem with a gas station letting me get water. I have my own hose, am buying gas, and offer to pay for the water. (I've never been charged for the water.)
Dump stations usually have water as well in the same general area. RV campgrounds will usually let you dump and fill the water tank for a small fee. It just hasn't been a problem.