End of May/beginning of June I'll be travelling West in Australia and I want to visit the Kimberley. I don't have a vehicle and I'm on a modest backpacker budget so where do you suggest I go in the Kimberley and how easy is it to see it?
If you're not flying in from Broome, then another great option is to take a charter flight from Darwin to Kununurra. It's the "main hub" of the Kimberleys. It's about a 50 min flight and more importantly will save you 10 hours of driving (you can also rent a car and self-drive from Darwin in about 10 hours). If you're based out of Kununurra it will be easy to use it as a base and see things like the Bungle Bungles.
I agree with Damien (below) that Broome is beautiful, but it's really expensive to get there from a flight perspective, and you will have a forced overnight in Perth if you're coming in from Sydney. You can fly directly to Darwin from Sydney and continue there as I laid it out above.
If you stay at backpackers place you'll get tons of fantastic advice from fellow travelers. Australia is an awesome place and everyone is super friendly.
Have fun, cheers!
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Broome is the main Hub of the Kimberley and is where you should base yourself if you don't have a car. Western Australia is vast so travel without a car can be difficult. It will take 2 full days of driving to get to Broome from Perth - that's 10 hours a day solid driving with stops only for fuel. It is expensive to fly there but you may get a deal if you're lucky. There is much to see in Broome and there are plenty of tours you can take from there as it is a tourist hub. You can see killer crocodiles, ride camels on the beach, the scenery in the area is amazing. I would suggest you team up with some others doing the trip to save transport costs by looking on crowdsurfers or some other forums.