When we bought our house not too much consideration was given to the backyard. The more criteria you have when searching for a house the harder it makes it to find something suitable and we already had enough criteria to make it hard. As long as the backyard had a decent area of space which was level with the house we were happy for the moment.
What we got was an undercover area, with some flat paving extending from it which was good, but a large amount of tired garden and with a rock retaining wall beyond that which took up a lot of space. It seems it was a case of when the house was originally built the block wasn't leveled all the way to the fences which would have been a cheaper way to deal with the sloping upwards of the block.
The garden also included a nice collection of ponds which water could be pumped through and cascade down.