First off, CX F is as good as it gets. Enjoy your PJ and real blanket/pillow. Stop at the AA lounge, do not leave the AA terminal (you may not get back in), CX lounges at LAX sucks. About 90 minutes before depature, you should head to the intl. terminal, sometimes the security takes 30 min or so - that terminal seems to have about 10 747 departing in the same 4 hour slot at night, so it will be chaotic (you can get a taste of Hong Kong right there). Tell the FA's it's your first time on CX (F), they'll take good care of you. Don't miss Green Wing on the tv-on-demand, if you're into British sitcoms.

Since there is no arrival lounge at the HKG (which is so weird, since everything else is top-notch), you may consider hitting an up-scale sauna in Hong Kong. Many have excellent showers (w/ toothbrush, razors etc), dry saunas, steam rooms, jacuzzis and a lounge with a tv. Expect to pay about $40 for 90 min of massage and you can hang out there as long as you want, sometimes even get free food, perfect for recouping after a long flight. Note that they may have different types of massage (wink wink), but they're not pushy about it.

If you like Cuban cigars, that's easy to find in HKG and they're reasonably priced too.