I would recommend staying in Randy's place in east Perth. It is great for one or two people. The apartment is small and simple, has a small kitchen with an induction plate, has a good shower, has 2 twin beds in a small bedroom, and is free of clutter.
The apartment is within walking distance of the river/
Easy access to downtown (about 20 min walk or one can jump on the frequent free Perth shuttle buses that stop within a block or so).
Randy is a very nice host, friendly and responsive.