What is the best way to get to the Great Barrier Reef from Sydney? Do you also have any recommendations on dive boats/live a boards?
If you have time you can drive (3/4 days drive) up to Airlie Beach and then get a boat from there. Petrol (Gas) is fairly cheap and its a beautiful drive up the east coast of Australia with loads of hotels or camp sites you could stay at. Otherwise try an internal flight to Airlie beach with Virgin Blue.
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We flew to Cairns from Sydney. We did an all day snorkeling tour with Silver Swift and booked ahead before we got there. There are a lot of different tour companies so do some research on which best fits your needs. We had a great time with silver swift. All day tour with lunch buffet and went to three different dive spots. We opted for snorkeling but you can also dive within the same group. One piece of advice is check out the Entertainment book available in several different cities in AUS. There is one for Cairns/Port Douglas and it saved us 30% on our snorkeling trip. It cost $45 to buy it for our phone and saved us $100usd. We also used it for restaurants during our stay so it was definitely worth it.
You will need to fly to Cairns and take a boat from there. There are many outfitters but please be careful to research and get local recommendations. Rely on Trip Advisor and the recommendations. I went from CairnsCairns on a highly recommended local boat. I am certified to dive but everywhere I go, I always enlist a private Dive Master because I don't know the waters. Actually I do this as well when I go skiing on a new mountain because I don't know the mountain. I rarely complain. But I had a "hot shot" foreign speaking Dive Master who obviously wanted to go diving more than be a guide. I did not have a good experience at all. This was a dream and spoiled by a lesser trained guide. Only reason to share is not to have others repeat this. Think about your level of skill and comfort and go on a boat with like minded divers. I would not recommend you spend any time in Cairns other than diving. It is a TShirt Tourist place so stay, find the very best boat and staff possible and then leave. SydneySydney and surrounds are wonderful for the land travel. Should you have time, you may wish to go to Port DouglasPort Douglas from Cairns... a lovely little village and one I think you would enjoy.