My personal favourite meat market in Sydney is Pendle Hill Meat Market (142 Bungaree Rd, Pendle Hill, NSW 2145). They have an amazing variety of fresh meat, as well as deli cuts, cheeses, frozen foods, bulk specials, fruit and veg, and even their own bakery, which serves the most amazing home-made pies! They also have a specialty section for game meats, and their own specialty sausages, such as 'parmagiana' (chicken sausages with cheese and tomato, crumbed!).
This is really the only meat market I know of, but I've never really ventured outside of my 'local' area.
I used to like Byers in Rozelle, yet they're now closed. I buy lilydale Chicken at a milk bar in Annandale. Otherwise Thomas Dux at Surry Hills is great. I don't cook meat very much at home, if at all at the moment.
If you're looking for something up-market, there's a meat boutique (yep, I said boutique) in Woollahra called Victor Churchill. It sells the highest quality Australian meat and gives you heaps of information about each cut. It's expensive, but worth it for something different.
Webster's meats, North Rocks Rd, North Carlingford Shops. These guys are multiple award winning champions of gourmet meats. Yes, they are VERY pricey, but their butterflied lamb for the BBQ and their range of awesome sausages are to die for!