I think you should use the BOGO for the IC Sydney, booking a club room. This club lounge is one of the best in the IC portfolio with stunning harbour views that you will treasure as a memory. If it is a trip of a lifetime, shell out and make it so. If it is your first and only time in Sydney, Coogee is an odd place to stay.

I hope you realise how far north of Sydney Cairns actually is! I would suggest not staying in Cairns at all (not an inspiring place), but at one of the resorts along its northern beaches e.g. Trinity Beach. Tripadvisor will point you towards some stunning apartments that you can let at a relatively low price. Still easy access to the Barrier Reef cruises and rainforest cable car etc.