If you want to see them the easy way you could not do better than to go to Kings Park which is literally on your door step. From the first of September it is spring and officially the park celebrates it with beautiful displays of flowers native to Western Australia all month.
It really is a concise version of all over the different climate zones. The everlastings are planted in swathes and drifts of joyful pink and white, all the varieties of kangaroo paws are on display. There are a number of parking spots sprinkled throughout the park and every single area has displays within easy walking distance. If you go to the entrance of the park into the information booth they not only have maps but at around 10 in the morning there are free guided walks and you can find the spider, donkey, cowslip orchids as well as masses of pink fairy orchids all over the place.
My favorite place for a coffee in beautiful surroundings is the Zamia Cafe next to a lovely kid’s play area. Good food,coffee,cakes etc for the same price you pay anywhere here.
You could go to Mount Barker, down South about 4-5 hours drive. But a condensed, very lovely version of anywhere is in Kings Park which we never tire of. If you have transport,try a days outing toward Cervantes, the flowering is more advanced further north and it is easy to find, a couple of hours drive and whichever area you go to there will be flowers!