In decending order, as it were:

10. San Diego International, AKA Lindbergh Field. It's close to the city proper, making for very serious restrictions in how and where you can fly, and with a peak of 55 comings and goings in an hour, all on a single runway, the air is more than a little congested.

9. Madeira Airport, AKA Funchal Airport, Madeira. It's runway runs extends out over the ocean, so a quick dip may make an unpleasant ending of the flight. It is also located right next to a mountain, leading to rather horrifying winds, that can and do change directions in mid-landing. And, the location next to the ocean also makes for lots and lots of seabirds.

8. Eagle County Regional, Colorado. Located in a high-altitude valley in the Rockies, the weather is capricious, to say the least. Being in a valley limits the space you have to move in. The fact that it is also high up means that flight in general tend to become a massive hassle, and even more so on take-off and landing.

7. Courchevel Airport, France. Located in the French alps, again giving you that ever so lovely lack of power, it's built more or less right into a mountainside, and has a runway that is scarily short. But the foremost feature of this place is that it is, as said, somewhat like landing and taking off on a rollercoaster ending with a ski-ramp carrier.

6. Kai Tak, Hong Kong. As mentioned, Kai Tak was right smack in the middle of Hong Kong harbor, meaning you approached at practically touching distance from raised walkways, in between high-rises. It also was a 'checkerboard' visual landing, as you had to make a turn in towards the runway, meaning you aimed for the checkerboard, made your turn, and really hoped you got it right, because there was no way you could easily say 'screw it' and try again.

5. Gibraltar Airport. Located at The Rock on the tip of Spain, it's a British holding. Locacted right at the 'mouth' of the mediterranean makes it attractive to the military, and the airport is shared between civilian air and the RAF. The ocean is RIGHT at both ends of the runway, literally, and right next door is the eponymous mountain, making for both yachts as floating barriers, and weather and wind that are, shall we say, less than ideal. As Gibraltar is on the tip of Spain, but is British, the diplomatic tensions are high, and Spain has restricted the airspace, which of course means flying in and out is EVER so much fun...and then, of course, there is the 4-lane highway that crosses right over the runway. There is an interesting creation.

4. Princess Juliana, St. Maarten. A high-traffic tourist resort and transport hub into the rest of the Carribean, the airport runway points straight into the island mountains, meaning you need to get your fully loaded aircraft up high very quickly, on the one side. The OTHER end of the runway ends with a road, 50 feet of beautiful white sand and then the turquoise water of the ocean, lovely to SWIM in but less fun to end up in as a passenger. And, of course, as with most tourist locations, space is at a premium, meaning that the hotels line up along the runway too. Makes for a great place to take pictures of the planes, as they pass right overhead on approach, but less fun to land the monster.

Incidentally, it's also the home of one of the most stupid things ever. With the short distance between the airplane ready for take-off and the road, and beach, people climb up on the chainlink fence that separates the airport from the road, and then try to hang on as the passenger jets spool up for take-off.

3. Gustaf III Airport, AKA St. Jean Airport, Saint Barthélemy. This airport is strictly for Carribean puddle-jumpers, but even with THAT restriction its runway is INSANELY short. This, along with the approach that passes downhill RIGHT over traffic, as in within feet, encouraging you to perhaps go a bit higher up, and thus further down the runway, has led to more than one plane ending up in the sand after not stopping in time.

2. Toncontin Airport, Honduras. Described as 'an accident looking for a place to happen', Toncontin has the shortest runway of any international airport in the world. It's placed in the Honduran mountains, and requires a step-down approach, the ground is about 150 feet from the airctafy on approach, but the airport level is 600 feet down a sharp drop, and then it all ends ends with a cliff dropping off at the end of the, short, runway. Similarly to Kai Taik, it's also a visual approach, requiring step-by-step hunting and finding for landmarks. And, as all airports located in mountains, it has weather that can change practically in the blink of an eye.

As an aside, Toncontin has the IATA airport code 'TNT'...

And proudly occupying the number one spot,

Tenzing-Hillary Airport, AKA Lukla Airport, Nepal. The location for Mt. Everest base camp makes it a popular airport, but located HIGH in the mountains of Nepal, it brings pretty every problem you can imagine. 30 flights move between Lukla and Katmandu every day, and there's only 85 miles between the two places...but the weather can be as widely different as it possible.
It's also at a VERY high altitude, and so airplanes have severe problems handling the flying. The runway has a gradient of 12 degrees, making the height diffrence about that of a 10-story building. You land uphill, something that pilots are very grateful for, because if you overshoot, the end is right into a cliff, making a very blunt statement. There is no overshoot, no go-around, once you've started your approach, you are commited and had best hope the gods favor you today.
Of course, in the OTHER direction, it's a sheer drop for longer than the runways length, which means that the potential extra speed you get taking off DOWNhill is as welcome.

For those interested in watching the show,
https://www.youtube.com/watch?v=T36xY3sQFEY

...!
Gott's Leetle Feesh in Trousers!
Boy am I glad I don't fly through anything scarier than Heathrow.