What a great thread. Loving all the photos!
We have been in Brisbane for 18 months and have rented in Toowong, Paddington and Graceville - all lovely suburbs but Paddington is definitely my favourite. It was the most friendly, and as we were on Latrobe tce, the shops, cafes etc made lovely social connections very easy.
Toowong has good transport links with regular buses, trains and city cat. The walking/cycle track has had an upgrade and runs alongside the river to the CBD. Toowong shopping village is good and never very busy. It is very close to Indooroopilly shopping centre too which has some lovely shops.
Graceville is quieter. Apparently the local state primary school is good. We paid $830. pw for a standard Queenslander. You have to be careful though as parts of Graceville are prone to flooding. Regular trains make it an easy commute to the CBD.
Good luck with your search!