well this is sydney so you will have to travel no matter what so the LDS i suggest are a little away from you but you are going to get that with any shop.
some i can recommend is:
Frogdive Willoughby, go in and talk to them, they have a strong club base dive schedule, weekly boats and monthly bbq & shore diving.
Many Dive or Bondi Dive. They very close to the dive site and they use a mini van to transport you from their shop to dive site. They both have huge tourist markets so their dive sites arent too challenging and you might appreciate that.
Another to check out is Deep 6 Diving at Ryde or Dive 2000 at neutral bay, but i havent been there for a few years but when i use to go there they always seemed very good.
there might be some dive shops in the northern beaches area but i dont venture that way often.
Hope these give you a start and enjoy