Asia - HKG, Taiwan, Thailand order of visit?

I am in the planning stages of this year's trip to Asia. I want to give the CX F class a go and as I have not been to Hong Kong before I want to spend several days there. I also want to spend some time in Taiwan and revisit my usual haunts in Thailand as well.

Any thoughts on which order to visit them in? I will use AA miles for the CX flight and have enough UA miles to fly *A back from BKK. So my original plan was separate one way awards USA-HKG and then return BKK-USA and I would pay for tickets between the others (HKG-TPE and TPE-BKK).

Does it make more sense to do something like fly USA-HKG-TPE on one award, fly TPE-BKK and spend time in Thailand , then another one-way ticket BKK-HKG (maybe the EK A380 suites?), do my time in Hong Kong and return from there (again on CX award)? I have plenty of flexibility with enough UA miles and AA miles to do just about anything. I can even use BA Avios for the short intra-Asia flights if it's worthwhile. I will be going in late Oct-mid Nov.

I am thinking it probably doesn't make any difference but just thought I would see if anyone sees pros to a particular way to go in visiting these three.

Use your CX miles to book a ticket US>HKG>TPE

7 days in HKG is a lot and will know the place inside out and upside down after 7 days, there is far more to see in Taiwan if you have the time.

Thanks. I ended up using AA miles to book JFK-HKG-TPE on CX F on the 773 and C on the A330. Had to pay cash for DCA-JFK because no saaver aaward seats were aavailable. I'll be in Taiwan for about a week. Then used Avios to go TPE-HKG (9000 for business class) on CX (currently scheduled to be the new config 773). Will be there for 5 nights/6 days. Then doing the EK F suites on the A380 to BKK ($640). Will be in Thailand for a couple of weeks. Then used CO miles for BKK-PEK-IAD in TG C (2-class A330) and UA F on the new config 777. So, about $1000 total plus 67500 AA miles, 70000 UA miles and 9000 Avios.