If there is anywhere in Perth you should check out, it's Kings Park. With spectacular views of the city and a feeling of doing something good for your body (there's a lot of uphill walking), it's definitely a must do.
We spent the good part of a morning there and only left because we forgot suncream. 'Coz it's so high there was a really nice breeze and it has some places to eat if you can't be bothered taking a picnic (Which I definitely recommend you do!)
I can't believe it took us a whole 2 months to actually make our way over to it and I think I left a little bit of my heart up there.