It needs to be said: Edinburgh Airport is not a hiking airport. It's the typical one-terminal, two-level airport, with one building that can be crossed within a couple of minutes. It has only one parking garage and little else. It is, however, the airport where I spent about one third of my leisure time in the past few years (the other thirds on mountains and golf courses, just to be complete). So, yes, this is not an entirely objective criterion; and I need to find better ways to justify this entry. Why is Edinburgh relevant from a hiker's perspective?
I could for example argue that Edinburgh is nicely embedded in farmland which serves as an ideal outback for any hiking adventure. While the north side is blocked by the runways, everything towards the south is open and mostly accessible. It is completely unproblematic to get to the airport on foot, an outstanding feature in a world where airports are typically surrounded by dense cobwebs of motorways. You will pass old stone cottages, cross fields, and occasionally see extremely wild animals (horses, just to give one example).
For I stopover of 1-2 hours I recommend to explore the area towards the southwest - there is the Royal Highland Centre, some sort of village called Ingliston, and even a golf course next to Fairview Av. The southeast is mostly covered with huge, flat parking areas, I mean, if you like cars, why not. The parking area directly next to the M8 motorway that limits the immediate airport area to the south has a bus terminal which is served by various city bus lines, which are millions of pounds cheaper than the Airport Express.
If you have more time, try to cross the double-laned motorway. This can be done anywhere you like in a dangerous, adventurous style, or more conservatively by using the tunnel between the two roundabouts where the airport access roads meets the motorway. Feel free to walk a figure of eight around the roundabouts. If you are finished, try to hike across the fields to Ratho, a few kilometers to the south. It has a pub, a canal, and houseboats. Show me any other airport with houseboats within walking distance, please.
The shortest meaningful excursion you can make is to the main control tower, just a five minute walk south on Jubilee Rd., that means back towards the entrance. The shiny tower looks particular shiny in the dark; the lightning at the bottom makes you think that it kind of hovers above the ground. Things hovering above the ground are always fun.
The terminal building, by the way, has a few niches for sleeping, particularly on the upper level to the right. It is not perfect, but sleeping is so 2006, anyway. Today nobody sleeps in airports anymore. How did I manage to write so many things about such a small airport? It's a mystery.