I'd usually recommend a trip to the Blue Mountains from Sydney, one of my favorite places there, but you'll be there in winter and they'll be snow on the ground there (3,000 foot level, 2 hours out by train from Sydney). It would still be a nice trip, and there is a visitors center and food court across from it, but will likely be too cold to get out on any of the trails.

There is plenty to do around Sydney. There's a marketplace in Chinatown (Paddys Market) that sells all the T shirts and souveniers you would want to bring home, but it's not open everyday. Hopefully you'll be there on one of the days it is running. On Sat and Sun there is an outdoor market with a lot of crafts in The Rocks area. Don't rule out the Taronga Zoo, also. They also have a maritime museum in Darling Harbour that's worth a visit.

I've always booked my tours after arriving, so can't help with what's available in Port Douglas (I always stay in Cairns). I think Letiole stayed there last year and wrote a trip report. You might search for it.