Is there any way to leave HKIA by foot?
I have a 4 hour stopover, so I would like to shortly visit the neighbouring city of Tung Chung (home to 200-year-old forts and temples), but I want to avoid the hassle of withdrawing the few Hong Kong dollars needed to go by bus. I also like the challenge of leaving airports by foot without using any money.
Walking directions for Google maps says yes, it's possible: https://goo.gl/maps/MVoPY
57 min, 4.6 km from Airport station to the center of Tung Chung.
Now I haven't tried this myself, and walking directions remain officially in beta... but a random Street View sampling indicates that the suggested route does have pedestrian walkways of some kind, including on the bridge.
I'd still exchange a few HKD if I were you: it'd be a shame to visit Hong Kong without eating anything, and you can take bus S1 back to the airport.
(Obligatory disclaimer: I work on maps at Google.)
Hong Kong airport is on an island. There is nothing else on that islands except an exhibition center and related activities (ferry terminal, hotel, …). In order to go anywhere interesting, you need to cross to the neighboring island of Lantau, Tung Chung being the first neighborhood when going from the airport to anywhere overland. While I think there is a pedestrian walkway along the western road bridge, I doubt that it's a pleasant walk (though a Wikivoyage contributor describes it as “nice” — I'm guessing this refers to the view rather than the ambiance), and it's a minimum of 4km from the airport terminal to the town (more like 5km to get anywhere interesting). You can check Google Maps (complete with Street View).
With only two hours' layover, taking account the time to go through security, you do not have time to walk. If the two hours are rounded down, you may have time, but walking isn't the best use of your time.
There are frequent buses between the airport and the Tung Chung MTR station, but they are not especially fast. If you take a bus, note that you can you can only pay by Octopus card or exact change. You can buy an Octopus card at the airport, but I don't remember if you can pay with a foreign credit card, and it has a HK$150 minimum value (you can redeem the unused portion afterwards minus a small charge; in comparison the return bus fare is HK$7).
The fastest way to get across to Tung Chung is a taxi. You'll need cash for that.
I have a 4 hour stopover
Which is not enough time to do much outside any major airport, especially on foot.
Assuming the 4 hours is arrival to departure time, consider the following:
You have already checked in for the departure, but you need to deal with security (5-30 min) and walking to the gate (5-15 min). And you need to be on board at least 15 minutes before the actual departure time. So that's another hour used up.
In total, there is an hour at each end needed for airport mechanics, and as others have calculated, it will take an hour to go anywhere (and the same back). So you have used up all your layover time and seen nothing - the area near the airport is all new-construction hotels and residences for airport (and hotel) staff.
Back when Kai Tak was open it was quite different - you could easily walk from the terminal to most places in Kowloon and be back in 4 hours. Security was much faster then too.
Nothing to add to Gilles informative answer - it's fantastic information that there is a footbridge (but for the OP's question, a four hour stopover does appear to be too short).
However, if you're staying at one of the the two airport hotels, such as the SkyCity Marriott, here's what would be a terrific "urban jog" which is a 10k, making the Novotel on the other side your destination. Enjoy.
It won't be possible. The roads near the airport are very complex and there are plenty of junctions. It's very hard to navigate between them. There is a sidewalk at Chek Lap Kok South Road but no one uses it because it is too far away. it takes more than 1.5 hours to walk from CLK to Tung Chung. Taking a bus only takes around 10-15 minutes.
