There have been a quite a few places that I have visited for breakfast, so far my favourite is Sayers. They have delicious breakfasts and amazing coffee. There is a Sayers in Leederville and one newly opened in Northbridge.
I love so many! Cafe Elixir in Wanneroo, Etro in the CBD, the eggs Benedict at Hardware Cafe is awesome, the Beach Shack at Hillarys is fabulous for crispy bacon. I've found a lot of great quality restaurants for breaky in Perth.
There are many I like in Perth, However I am finding that I keep going back to Miaflora (alongside a beautiful nursery in Beaufort Street).
The service is not so good on weekends however they are the only ones I have found who do "mini" serves and instead of getting two eggs and two toasts, etc, you only get one which is sufficient even for me, who is a greedy eater and generally eats too much!