Paddleboard Lake Wivenhoe, usually all to yourself!
Lake Wivenhoe is a great recreational water location.
There are rules and regulations on where and what type of watercraft can be used on the lake as it also supply's most of Brisbane's drinking water.
While that means you may need to check up on the latest guidelines before you go, it usually keeps water traffic down to some sailing boats or kayakers and not much else. I have been on week days and been the only one out on the water.
Cormorant park has great amenities including kids play area, BBQ's, toilet facilities, weekend café and great views. I usually park here and walk down to the access area to get started. I will point out that the bottom of the lake is not that great underfoot, and that I would make sure you can see the bottom to be clear of rocks or old logs if you think falling off is a possibility for you. Confidence on your paddleboard is probably required due to this reason or if you have time to find a nice clear spot it would be good for beginners.