I am in Canungra, and yes, Logan does a bus service to beenleigh daily.
As far as I know it is not regular in as in maybe once or twice a day. So you may be stuck at beenleigh for a while.
Also, I don't think rent is not super cheap either, but it is an awesome town and we love it here.
Maybe Jimbooba? Not as pretty, but better services.
There is also a local bus driver in town who travels to the coast (Nerang way) weekdays as he does a school run and I am sure he would take you, but once again, it's an all day thing.
Maybe park ridge, or greenbank or edens landing. Over the othe side of the highway is Jacobs well and willowvale also now has great facilities.
Can you get some one to take you for a day trip drive?
Eta, whAT ABOUT ONE OF THE NEWER SATTELITE suburbs like springfield?
they have awesome facilities, parks, shops, transport etc.
Not so much rural, but very nice, all the same.