Naturally, all of these are my opinions and are quite general.
- The more natural light an airport has, the better.
 
- Higher ceilings / atriums and better design for large passages, cf. lower ceilings and rabbit warren like pathing.
 
- A transition from landside to airside that doesn't force you through retail (viz. duty free), especially retail where the pathway through it is not clear, the exit is not immediately apparent and is crowded so the traffic throughput is quite slow.
 
- Gate placement from central areas/hubs/masses of activity. Bonuses for use of moving walkways, shuttles etc. to effectively reduce the time to very far gates from higher pedestrian areas (e.g. exit of security screening to airside). This includes similar assistance devices for arriving passenger flow (i.e. to arrival procedures).
 
This is why I believe HKG is an effective airport based on these criteria. SIN also is fairly good in these respects, putting aside the debate of whether people prefer the T1/T2/T3 security model (also see KUL T1), or the T4 security model (more common around the world). Without being too ostentatious, I also think HND T3 is quite nice and checks many boxes.
In Australia, the best international airport in accordance with these is probably a toss up between BNE I or SYD T1. That said, I haven't visited the other international airports for a long while. Comparing BNE I and SYD T1 is also unfair because they handle drastically different volumes of passengers, plus BNE I is undergoing a renovation (and who knows, masterplan may relocate it out towards the current BNE D QF side).
Other things which include "would be nice" or are a bit unfair to include as criteria:
- Affordable prices for concessions and stores at the airport, especially that airside (yes, we know we are "trapped")
 
- On that note, a good array of different stores, particularly for food and drink
 
- Enough waiting seats near gates. I suppose one should also ask for plenty of USB charging ports or power sockets, but.....
 
- Decent (fare prices, safety and convenience for passengers) public transport to and from the airport to the city centre or important and accessible transport hub
- An accessibility thing, but free wifi should extend out to the rideshare vehicle platforms. I'm surprised how much this isn't a thing.
 
 
- Premium passenger pathways through the airport, either for specific airlines or all airlines. While we tend to love these, it's not fair to give a lot of weight to them because naturally many passengers don't give any regard to such features.
 
- Good and efficient organisation of queues and minimisation of wait for, especially, security screening, immigration and customs.
 
Things like HKG's Skybridge are fantastic, I love the novelty of it, and it's definitely a draw for the airport. I wish there was more than one restaurant or concession or even a sit down area up there, but it's still a great feature. Does it 
alone make HKG a great airport? No, of course not. Should every airport in the world have a skybridge? Again, of course not (aside from the fact it wouldn't be practical in many airports).
A good lounge can make an airport desirable or great for us, but since not every passenger can access an airline lounge, it's a bit much to simply boil down how good an airport is based on the lounges (or a specific lounge) it has, even if that may be the only place that a given passenger may spend the majority of their time at said airport.