Where is the closest bike track to Balmoral?

There are limited bike tracks. You can ride the riverside from Apollo Road ferry to Hawthorne ferry. Some parts through parks/boardwalks and some parts on (very quiet) roads. Main linkage to the city is not easy - involves getting to the bike track at corner of Hawthorne Road and Wynnum Road. Either footpaths or riding on road - with some hills. Plenty of people commute it on a daily basis, but its not a 'recreational ride'.
If you want to get completely off-road, you can go to Murrarie recreation reserve, there is a cycling track there - used for races on Saturday mornings but otherwise is open for anyone to ride.