The Avoca Lodge is located in the heart of Randwick, across the road from the hospital but also a 1 minute walk to the Spot - a great location for eats! The Randwick junction is only 3-5 minute walk and that will service any other need you have including access to public transport. Beach is 20 min walk (downhill).
I stayed here to help me as I was moving in nearby and I ran into trouble with delivery. The staff at Avoca were extremely understanding and let me extend my stay on short notice without issue, shuffling around other checkins to avoid any double books.
If needed I would happily stay again. Bed is big and comfy and room is air conditioned + wifi available.