Both HK and Taipei have things to easily do beyond the city bustle experience. Having explored Taiwan a bit, I now only recommend people base themselves in Taipei and explore from there. The metro will get you out to xinbeitou for a hot springs experience (with the local pensioners not tourists) and to the zoo to take the cable car across the tea plantations for a tea house experience at the far end. And I recommend the Longshan Temple night market.
Similarly in HK I'd take the ferries out to Lamma island, do the easy and obvious walk across to the village at the other end for the ferry back. And the cable car on Lantau to see the tian sian buddha. As well as going up the Peak with the tourists - the bus is often quicker than the queue for the peak tram, and shows you other areas on the way.
This commercial free guide to Hong Kong is a labour of love by whoever is responsible for it & well worth a browse for anyone going there.
I recommend getting an The Octopus card even for a few days - makes travel a breeze & the public transport is excellent. Impossible to get lost & if you get wet, you have gone too far.
Taking buses to the beach at Shek O was very enjoyable.
Get thee to anywhere in Asia. Your previous posts indicate you plan to stay in Australia for a longer period, so you're likely to buy a one-way ticket. There is a lot of traffic between Australia and Asia, so fares between destinations in Asia and Australia are reasonable. Check it out on Skyscanner or Kayak.
Hong Kong and Singapore are expensive places to visit. But Bali (Denpasar) isn't pricey; and nice to spend three days before continuing on to Oz. It's popular with Australians; and you might make some new friends there. Bali is a major international tourist destination, so there are lots of flights. There are many other places in Asia to choose from. So imagine where you'd like to be.
[ Edit: Edited on 09-Apr-2016, at 03:58 by berner256 ]
The reason I was thinking of Dubai is because I only have 3 days in wherever I stopover. Places like Hong Kong, Singapore etc I will be visiting at a later date during my travels and for a longer period than three days, so I would rather not waste the three days in these places when I'll be seeing them anyway for a longer period. I thought Dubai would be best as I only have three days and that seems to be all the time you need there.