There are possibly too many to choose from. I love the beauty spots by water, so Bells Rapids in the Swan Valley, Serpentine Falls, the waterfall in Lesmurdie and the view of Helena Valley from the reservoir. However for gorgeous countryside, Chittering Valley and the Avon Valley are just stunning. It's so difficult to pick a favorite in such a gorgeous state.
Anywhere along the Swan River, where you can sit and enjoy the tranquility of the water and watch the birdlife is relaxing. My favourite spot is at Point Walter, where you walk on a sandbar out into the river and you feel as if you are in the middle of the water. A popular picnic spot and you can look out across the river to the expensive houses on the other side.
Anywhere along the Swan River or along the beach. There are so many lovely parks and picnic areas! Some personal favourites are Cottesloe Beach and Burns Beach. I find it especially magical to turn up in the late afternoon for a swim, and then just lounge on the beach, watching the sun set over the ocean. The Perth Hills are also really special...especially after the winter rains when the rivers are running and the wildflowers are blooming.
Finally...don't forget Rottnest Island! When I feel tired and run down I like to take my bike over there and cycle around the more isolated areas. When I find somewhere peaceful, I'll pull over and soak in the beauty for a few hours.