Well Pitt street mall is good place to start & isn't far from george st, just around the corner. George st is great for Adult shops if your interested LOL!
Darling Harbour is just going to give you touristy stuff I think. But if you are up to walking there is heaps to see. Um the Queen Victoria Building would be another good spot. I am sure there are a few babyish shops in there. But would be mostly designer types.
I don't go into the city all that often so I don't know all the places to be but when we do go, there is 2 places we head both for DH. 1 is a comic book store & the other is a book store that is so big it takes up the top floor of one of the shopping centres, its near the QVB I think but not 100%. So we go to these two places then just wander around for the day!

Have fun!