There are basically 3 parts of Sydney that draw backpackers. The city center, Bondi Beach, and Kings Cross. Each has it's own set of appeals, and Kings Cross puts itself squarely in the middle of it. Unfortunately, the Cross has a reputation of being pretty rough-and-tumble, largely because of the 2-block Red Light District along Darlinghurst Road, but it's otherwise a very nice area, and the Pink House is probably the nicest of the hostels in it.
Set back behind the local police station and the famous El-Amein fountain, The Pink House is quite literally a pink house - actually, 2 of them joined together - reminiscent of the many house-like hostels found in the Bayswater section of London.
The rooms are pretty basic, and the bathrooms - while clean - can be pretty cramped. The kitchen's fairly small as well, but definitely useable, and the free breakfast (toast, coffee, tea, cereals, etc.) makes it worthwhile.
What the Pink House lacks in facilities, though, it makes up in social life. Most hanging out occurs around the back yard picnic tables by day and the living room by night, and there's almost always someone friendly there to talk to and hang out with. A good portion of the people staying at the house are long-termers, so while they may not be up to party every night, they know the city WELL and can tell you the best way to get places, the best deals around, etc.
When you do go out, it's pretty simple. The Cross is home to most of Sydney's backpacker bars, so finding a decently priced place to drink/eat is rarely an issue. And everyone's pretty happy to come back to the living room after bar time and drink the night away until dawn. This lifestyle is easy to get sucked into, so watch out!
Recommendation: If you want a big, hotel-like, centralized operation, stay in the city center. If you want immediate beaach access, stay in Bondi. If you want a cozy, relaxed base of operations with tons of people who just want to chill, the Pink House is the way to go. I wouldn't recommend it for anyone who just wants to spend a night or two in Sydney, but if you're there longer, this is a good place to make some friends and soak up the city.