Cairns is a great city for cycling because it is pretty flat.
Bikemap has a website and App with maps and information for getting around Cairns, its suburbs and further afield to the Atherton Tablelands.
Find it here: https://www.bikemap.net/en/r/3234078/#11.53/-16.9724/145.7505
There are lots of routes with information on distance, time and rise and fall along the way.
The map shows the route in blue.