Perth City is a big country place, if you are staying in the city, try the free walking tours of the CBD. Up in the hills of Perth you will find quaint little places that are great for food and coffee. I found an out of the way winery that I believe makes the best port... Jadran Wines, and its not far from the CBD.
In Fremantle, go to the prison and take the tunnel tour, you will be in a small boat and its very interesting.
Further afield at Margaret River, make sure you go into at least one of the cave tours and have a look at Boranup Carri forrest, majestic place.... oh yeah!, taste the food, wine, cheese and chocolate in that region. Swan Valley is also a great place to visit which is north of Perth and has all the Margaret River has to offer in food, wine, cheese and chocolate.
Broome is a great place to visit and if you get to do the drive on the Gibb River Road from Broome to Kununurra, that's a bucket list tick.