The YMCA in Kowloon would be a good choice for hostel-like budget hotel. Not near the airport, but transportation to/from is available 24/7. There's always the Mount Davis Hostel, supremely inconvenient, lousy hours, and haunted to boot!
Also not terribly convenient but really a cool place is the Shek Kip Mei refurb hostel:
https://www.yha.org.hk/en/hostel/yha...-youth-hostel/