I mean it kind of depends what you define as walking distance.

Google maps shows TLL-old town as 56 minutes

CNS-arbitrary point in cairns city (cairns base hospital- it’s probably the northernmost point of the city proper and is on the esplanade) as 1 hour and 6 minutes.
ADL- Rundle mall is 1 hour 30 minutes.
CBR- Parliament House is also 1 hour 30 minutes.

I wouldn’t fancy walking any of these in January!

BNE/PER/SYD/DRW/AKL etc all come out in the 2-4 hours range which I think we’ll agree is not walkable