Can't see how yo'd not have to clear immigration and customs in Hong Kong. Can't think of a single example of a "sterile" ariport hotel. As for Melbourne, cheap does not come easy in Australia. I always stay at the Hilton, just on the edge of city centre, but a nice stroll through the park into town, or a tram ride to the main rail station. It will be in the A$200 range unless you are there on a weekend, in which case a Bounce Back price is available closer to your target (assuming A$100, not US$100). Or you could get a HHonors 50% certificate if you belong to that program.

Regent, Hyatt and other are far too expensive. Sheraton have a massive hotel on the south bank of the river. As with Hilton, a 50% off certificate from Starwood might bring it down to your price level, as would a weekend stay.

Have a great flight(s).