The gym is always a go-to source for me. And when a hotel does provide free bottled water in the room I’ll usually hide any bottles I haven’t consumed in my luggage in case the hotel brings more. I wouldn’t want them to think I was already stocked.
In much of the world you can drink the tap water though whenever I’m uncertain I avoid it. I’d rather drink filtered water (hopefully they change the filters) and I want to use my own or a hotel-gifted bottle, not the hotel’s glasses in the bathroom which may or may not be clean.