Broome is gorgeous, but actually really expensive, because its a tourist town.
I would REALLY recommend Albany - I would move there if I could! Its about 4 hrs out of Perth, and, although it's starting to grow, it's still got a 'country' feel to it. Until about 5 years ago, there weren't even any traffic lights, only roundabouts! It's on the coast, so you've got great beaches that are pretty safe for kiddies - Emu Point is pretty sheltered, so it doesn't get big swells.
There's also HEAPS of natural attractions. You've got The Gap and Natural Bridge - part of the coast where the rock has been worn away over time, and the ocean comes screaming into a wedge in the coast line. On a stormy day you'll get wet from the spray in the carpark! The Natural Bridge is literally a bridge that's been formed over time, with a little cove now open to the sea. Some tourists go down into the cove, but I really wouldn't recommend it, as the water doesn't always come up, but when it does, it's very fast.
There's Whaleworld, one of the last operating whaling stations in Australia. It teaches the kids about what used to happen, and why we stopped. The old Fort, an army base from the war. Plus heaps of photo opportunities with natural scenery - we took 300 photos on our 10 day trip, and only 25 of those were us!
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