The hostel with the shortest distance to HKG appears to be the YHA Ngong Ping SG Davis Hostel, but not very practical to get there late at night (or even during the day).
If not sleeping at the airport you'll have to go to Mong Kok or TST. If arriving after midnight you can take the N21 bus which runs every 20 minutes, though don't know if hostels typically have 24-hour front desk....
Ngong Ping is very inconvenient. I think you can only get there by taxi late night. It may be closest to the airport, but it will still take 30-40min by car. I took a ride there about 14 years ago. IIRC, we have to go from North side (Tung Chung) all the way to the South side of Lantau Island before going back North the Ngong Ping on winding mountain roads. According to their website (
https://www.yha.org.hk/en/hostel/yha...-youth-hostel/), their opening hours are 7am-11pm.
I would not recommend hostels at that hour.