Agree with the others re swimming weather, but that is for us Perthites who like it nice and hot .

Things to do:

Kings Park - just beautiful, lots of different kids playgrounds and a couple of cafes, walking trails, great views - can easily spend half-full day there exploring it all.

Subiaco - Close to CBD of Perth, some great shopping - boutiques etc, lots of restaurants and cafes, on the train and bus lines, close to Kings Park, has Patterson Stadium (if you wanted to catch a game of AFL while here), easy to walk around. Train line from Subi will take you into either Perth or Freo so it is a pretty good place to stay but might be a bit exxy.

Fremantle - I am a Freo girl so am a bit biased . Markets on Fri/Sat/Sun. Lots of restaurants and cafes, a few good boutiques (Market St and South Terrace) and shops (arts/crafts etc especially walking down towards the Round House). Esplanade Park is a great big park for kids to run around and is right next to a couple of really family friendly big places for fish and chips - Ciccerellos and Kailis. Fremantle Prison is worth a tour and so is the Round House (original jail and the tour is free). The Round House is right on a small beach called Bathers Beach where kids could go for a bit of a paddle. All of these are walking distance from the train line. Has a couple of dept stores like Target and Myer. Great great pubs - I personally like The Norfolk and Little Creatures Brewery - has a sand pit and small play area for kids out the back. A 5 min car/taxi ride out of Freo is another great Pub by the river called The Left Bank - we take our kids there for meals a bit and they love it. Wakling along the same part of the river there is another cafe called Zephyrs which is located next to a playground, serves good brekkys and coffee and once again my kids regularly go for a paddle in the river here as it is nice and calm. Is a great spot to sit and watch all the million dollar boats go by.

Rottnest day tour - can be quite expensive the ferry ride but if you google rottnest island they sometimes have good ferry deals.

Mandurah - day trip, fish and chips by the water, playgrounds, lots of beautiful houses on the canals.

I don't often go north of the river so can't tell you much about that.

Perth Zoo is lovely too and you can catch a short ferry from CBD of Perth across.

Adventure World - not as great as your Gold Coast theme parks but they have recently upgraded it. It is also located right across a big lake called Bibra Lake where you can feed ducks and swans and there are a couple of good playgrounds.

Harbourtown in CBD Perth is outlet shopping.

Hmm thats all i can think of atm but feel free to PM me. I love Perth and for a nice relaxing family holiday would definitely recommend it.