really depends what you're looking for and how hardcore you want to be about it.

*Arrivals Lounge is practical....easy spot for both of you to meet, close to Airport Express, both of you will have access. However, there's nothing sexy about that place and it's very small and cramped. Definitely functional though and serves the practical purpose well.

*If you want to be really hardcore, are into the whole lounge thing, want the best "experience" etc., get your onward BP to BKK (and tell your father too as well) at your departure airports. With this, you'll be able to go through transit at HKIA and access the departures (airside) level above the arrivals level. Thus you both can access any of CX's lounges, including the Wing F if you want to use a Cabana, etc. Then, when you're freshened up you tell the staff you must depart the lounge and go landside. Fyi this is not a typical request but is doable. I personally have done this before, as have other posters I've read about on here. They will either give you a stamp, slip or accompany you, you then go to security who will let you back downstairs to the arrivals level. Then you proceed through immigration and visit HK before returning to the airport.

*Meeting at his gate is a cool idea. You could then do either the Arrivals lounge or the airside option above afterwards.

I caution the airside thing is a little extreme, this definitely isn't what CX is intending for pax, and personally I don't do it even if I have a long connection in HKIA. I can't recall exactly but I seem to remember I did it because I had a situation happen in HK that I had to go airside and attend to. I usually go into town or play golf at Sky City Nine Eagles (airport 9 hole course) with a connection such as yours. But just saying this is definitely doable if that's what you're looking for.