Recommendations on Singapore, Melbourne, Canberra, or Sydney

At the end of next week I am traveling again. This time I head to Singapore for a week, then Melbourne for a week, Canberra for a week, and Sydney for a week. Not really sure what I want to do while I am there (apart from teach a few Captaris classes). Does anyone have any recommendations for me? Is there anything I have to do while I am there?

Looking out to July, I am also heading to Oslo, Bangkok, and a return trip to Singapore. Recommendations for Oslo and Bangkok would be great too.