The Illustrated Man on Elizabeth Street. They are pricey, but (and I'm sure theres issues will be top of mind when choosing) SAFE, and true artists. I have seen some absolute disasters when it comes to tattoos and your'e so right to look for recommendations! Good Luck :)
Would love to know more myself. Surry Hills comes to mind. There are a few great tattoo parlours - think Crown and Elizabeth Streets. No names come to mind specifically. Only know the coolest tattoo joints in Melbourne (my previous home) at this stage after 18 months in sensational Sydders.