I'm not very good at sleeping on airplanes (at least in cattle class - I've never flown overnight on higher classes), and I don't fancy the prospect of sleeping for a couple of hours in an airport transit lounge either. If it happened on the way to my tourist destination it'd be fine, but unfortunately it's on the way back home (probably because my tourist destinations are further to the west of me than my home city), and I don't want to be half-asleep when I go back to work. Usually it takes me more than one day to recover from a red-eye flight, so spending two days flying non-red-eye may actually be better than spending a single day and night flying red-eye.
I looked up kayak.com for flying from Ulaan Baator to Sydney, or from Osaka to Sydney, without using a red-eye flight, and it said that there weren't any.
Is it possible to fly from city X to city Y during the daytime, have a good night's rest at city Y, and then fly from city Y to city Z during the daytime? How do I search for the most suitable flights, in terms of cost, and start and end times for each flight, and can I ensure that if the first flight is delayed for reasons beyond my control and I miss the second flight, I can get another flight without paying any extra?