Hi KSinNYC,
The SFO-HKG flight arrives HKG early in the morning and the Bombay flight is a little after 2 pm. That is one short stopover possibility in HKG to freshen up, see a bit of HK etc. But the HKG-BOM flight is via BKK and you can't get off the plane for 1-1.5 hours at BKK. So you could think of a BKK stopover too. Of course stopping for longer in HK itself is a good idea too.

By the way HKG-DEL is a direct flight so you can keep that in mind depending on where in India you want to go.

P.s. I don't think you asked about tours etc. in India so that's it from me for now.