There are loads of good places to sit (even in the food court when it's closed). A free little library which is safe and well lit. There are always nooks you can find that no one is sitting in already and the toilets on the upper levels are always clean. It's still a good place to tell the time too. The famous clock still works!
There are little sofas and quiet spots all around this awesome shopping complex. The Emporium is clean and well lit and the toilets are easily accessible. I think they are the cleanest toilets in Melbourne CBD. The food court has a great selection, uber comfy seats, is very clean and you can enjoy free wifi too.
This is a great place to go when it's either stinking hot or freezing cold outside. There are places to sit with kids and you can also use the wifi. Heaps of great places to sit and comfortably read a book or surf the web. You can also peruse some art, catch up on some reading, play some chess, or hang out in the kid's area. You must leave your bags in the bag lockers out the front though.
Fed Square is generally better in Summer, however, there are places to sit and read quietly where you won't be bothered. Better in the warmer months than the cooler months. A few places to sit and watch the world go by.