The best thing about Jenny's place is the location. It's a very easy walk to the King's Cross metro station/neighbourhood where you can meet many interesting people and get some cheap eats. Sydney is extremely walkable, and we had a great time the first day walking all the way to the opera house by way of the Botanical Gardens. If you don't fancy walking, you can easily take the metro to all the best places in Sydney.
One very nice surprise about Jenny's place was the wonderful sunrises over the bay, and the sun streaming in to warm up the balcony and living room. Sydney is very sunny, and Jenny's big front window collects a ton of it. Even better were the crazy gangs of cockatoos flying past the window in the morning - so cool!