I just got vaccinated at NTUH in Taipei. I…saw some room for improvement in the procedures. 
I showed up around 2:40pm for the afternoon appointment (3pm cutoff), which I booked a couple of weeks ago. Filled in a couple of forms (mostly Chinese only - English versions not available) and was given a queue number in the high three hundreds then directed to wait in a packed waiting/observation area containing maybe 80-100 people pretty close together:
Stood off to the side a bit because screw that, and waited for ~80 minutes until my number was called, getting my temperature and blood pressure taken in the meantime.
Was then called into another enclosed space with a dozen or so people before briefly seeing a doctor (his only questions were “Where are you from?” and “So you’re getting the vaccine from your own country haha”), filling in the vaccination card, and going next door for the injection. I was also given an appointment for 8 weeks in the future at this point.
Then went to the cashier to pay the NT$600. In contrast to what somebody else posted here, the cashier said that this was per dose and I’d also have to pay NT$600 at the next appointment. (Has anyone else asked at other hospitals?)
Then told to stay in the waiting room for 30 min (fortunately less busy at this point) to watch for adverse reactions, before being given the vaccination card.