wow 6 nights is quite a substantial trip. More than most people

Ok you should be able to cover a great deal of Bali then.
Refer to the map of Bali as you plan your itinerary. Have you made accomodation bookings yet? If that is the case, then you itinerary needs to be planned around that.
Ubud is quite central in Bali, but if you go to the very south of the island (eg Nusa Dua area), then it's still quite a long journey back to your hotel in Ubud. And if you travel at night, road safety is something to think about.
I think the safety of your belongings in the hotel is also related to how reputable the hotel is. It is not without risk of course. But on the flipside, if you carry all your gear and it weighs you down, it will be to the detriment of your enjoyment as well. I have been quite 'gung-ho' and left valuables in my luggage in the hotel room, and so far (touch wood) all has been ok. Not saying that this is definitely the way to go of course...
Toilets seem to be far less common than in Singapore, and usually much more crudely constructed. I remember the one near Ubud's famous babi guling ibu oka was a dark room with a hole in it!

So be careful if you have diarrhoea, then might be problematic.