I flown from Seattle to Manila a few times ...
SEA-TPE-MNL
and
SEA-ICN-MNL

flying again in November SEA-TPE-MNL

For the next trip, I leave Seattle at 12:30AM and arrive in Taipei at 6:00 AM, depart at 9:30 AM and arrive in Manila at 11:30 AM

I generally try and grab a short (2 hour) nap on arrival, and then I'm good to go the rest of the day.
I usually do pretty well the next couple of days, but find a short afternoon nap helps immensely.

On the return I leave at 12:45 pm, arrive in Taipei at 3:00 pm, depart at 11:00 pm and arrive back in Seattle at 5:30 pm...
In this instance, I'll have dinner someplace...
Try and stay up to about 10 pm or so and go to bed.

(Last time I flew through Taipei, I arrived earlier in the day, but the flight also left around 11 pm. The tourism authority offered a "free" tour.
So I took that... took about 4 hours I think. Left you at the 101 Tower where you could stay and then take the Go Bus back to the airport at your expense, or ride the free tour bus back to the airport - not sure if they offer this anymore or not)



As far as figuring out the time difference...
If we're on daylight saving time, just add 3 hours to the current time and switch it to the opposite am/pm...
If we're on standard time, add 4 hours..

So 9 pm here... is noon tomorrow there.
7 am here is 10 pm there.