In the Whitsundays, I definitely recommend a flight along Whitehaven Beach and out to the reef (Hook and Hardy reef).
Hamilton Island, (Great Barrier Reef Airport), is the most built up and has plenty of tourist infrastructure, a nice beach and free shuttle bus around.
Airlie Beach offers cheaper accomodation, and is more relaxed than Hamilton Island. The airstrip there is Shute Harbour, google whitsunday airport, local procedures on website.
Brampton Island is another option, the airport is on the beach and there's a resort as well as very basic camping facilities.
Lindeman Island also has a resort, but I'm not sure if it's open again yet.
With all these airports, phone/email ahead to get permission. Fuel available at Hamilton and Shute Harbour.
Feel free to pm for more specific info.