Public Primary Schools on North Shore (Sydney)

Hi!
We're moving to Sydney in 5 weeks and my husband will be working in North Sydney so we're looking at renting either on the Lower North Shore (Mosman, Neutral Bay) or in Manly.
Our 6 year old will be going back to school and we've got in touch with some of the public schools in the area, but wondered if anyone's got any personal experience. We love the look of Neutral Bay Public Primary and Beauty Point. Due to catchment areas we need to know what the schools are like to consider which areas to live in.

My husband's a surfer so Manly Village Primary and Harbord Primary are also possibilities. Any ideas or advice?

Help!!

Hopefully will catch up with you guys when we land!