There's several good hotels like Westin, Aloft, and Marriott near SFO, but the age issue does come into play. I think a good hotel would be worth every penny here.

I would call them and see if they'll take a 16 year old and have a 24 hour shuttle (the hotels are a mile or two off airport). If either answer is no, then I would change to a better routing.

Edit to add: I just looked up a random date in August and found an AA/CX itinerary STT-MIA-YYZ-HKG-SIN with the longest layover 3 hours in HKG. So there are other options.