I can recommend the CKS Hotel at Wolli Creek. It's about five minutes from the airport (about a mile), in the same street as the Novotel, and they run a shuttle to/from the airport. It's about a 10 minute walk to Wolli Creek station from where you can take the train into the city to Circular Quay (17 minutes). It's on the same line as the airport station. I've used it many times (lost count) to stay the night before flying out of Sydney (mostly international), and found it cheaper than others in the area.