I got certified out of Cairns with Pro-Dive. They run a really classy operation for those seeing to get certified while on vacation. They also do live-aboard trips with the M/V
Kalinda.
I just checked
Pro-Dive's website, and they show a 3-day 2-night trip for $520AUS (that's about $300-350US). I was on this trip for my o/w check out dives and had a blast! Staff was great, and the food even better. Worth looking into in my opinion.
As far as things to do while in Cairns....there's plenty. The Dreamtime center will teach you about the Aborigines. The Woolshed Bar is rocking everynight. Raging Thunder Tours has lots of things like white water rafting, balloon rides, and much more. And the Rattle & Hum has a good feed as does the Chapel.
And Be sure to check out the Daintree Rainforest. Guided tours are available and are very informative/well done.
Also check out Fitzroy Island if you want a little side trip. And if you take a Sea Kayak tour with Vince, you'll be very well entertained. And if you ply him with plenty of chips and beer, you'll laugh your self silly at all his Kiwi (New Zelander) jokes.
And out of Port Douglass, be sure to do a day dive out on the Quicksilver setup. *VERY* pretty reef with lots of life and they will also do discover scuba for any non-divers in your group.
As you can tell, I had loads of fun while I was there...and I'm itching to get back someday.