take the airport express subway line, for 70 hkd it takes you directly to kowloon, you can then take a taxi or another subway (not recommended during rush hour) to your hotel.
Must do? depends on what you like. you have to go on Victoria Peak at night if you're into architecture, best view of HK island. they just re-open the lift to the giant buddha statue (you may have to wait for more than 2 hours to get on). Or you can just walk allow harbour side and see and enjoy the view. I've always like the astronomy museum, and ocean park, but that's more kiddish stuff.