I visited Sydney and Bondi after my last visit to Melbourne and while I didn't spend much time there, I do have a few suggestions. Overall, I highly recommend you talk to locals once arriving- there are so many nice people that will share their tips and recommendations. Our Uber driver gave us a laundry list of places to visit in downtown Sydney on our next visit that I need to dig up, but for now, I will share what I can.
*By few I mean a zillion
Hard to share a ton here (again, we stayed for only 3 days) but we loved our AirBnB in North Bondi. It fit 3 of us very comfortably and is owned by Harry (who owns the coffee shop below). He is a delight to deal with and around for anything you need. The space is clean and very basic but we were barely there as there was so much to see, but it was centrally located and walkable to everything in Bondi. My friend and I Ubered easily to Sydney Harbor in 10-15 minutes while my insane husband walked the entire way to get some air, snap photos and go on a solo adventure. It took him awhile and his feet hurt like a bitch after, but he recommended it.
My friends who stayed in longer than us in Sydney highly recommended the Surry Hills neighborhood.
Overall, make sure you are somewhere near you plan to spend most of your time or near one of their public transportation offerings. Uber was very easy as well.