My suggestion would be to leave your luggage at the left baggage service in HKG and leave the airport and take the train to Kowloon (airport express). From the station there are free buses that go to the local hotels; take the bus to the Sheraton. HKG streets are full of life at midnight (in fact until 3 am) and lots of stores are open at midnight (even big stores, like Esprit, are usually open until 11 pm). Probably you got lots of sleep on the CX flight and want to walk around, see the sights, sample some fine food, etc. You can do that pretty safely in HKG (much safer to be walking alone on the street at night than in any US or European city). I'd walk from the Sheraton to the Peninsula hotel next door, tour it, maybe go up to Felix for a drink (one of the coolest bars in the world), walk to the Star ferry and ride it across the harbour (cost is about a quarter). Then I'd ride it back to TST though some would advise you to stay on Hong Kong Island. That side is more British and proper; the TST side is more chinese and progressively poorer and chaotic as you head into the fringes such as Mong Kok. A great experience is to walk along Nathan Road up to Prince Edward; if you are brave venture into the side streets. Lots of little stores selling everything imaginable (some quite good at good prices; for example I got a small backpack there for USD 4 and it is top quality, would cost 10x that in the US). Even if you don't shop the experience is quite something. If you get tired there are lots of small hotels around that are quite cheap (under USD 50), or you could book a room ahead using a web service such as http://www.asiahotels.com

Staying at/near the airport seems like a waste of time and you probably won't be able to sleep after the long flight from NY. A good long walk and some HKG nightlife is much better and it is so easy to leave HKG airport and get back there in the morning.