I just tried. It is surprisingly easy, and I would totally recommend it even if you have only 4 hours between flights.

I will suppose that like almost everyone coming from an international flight you are at Terminal 3. From the arrivals, go down to the ground floor, where the local buses are, and walk to the right:

After the last bus stop there is still a sidewalk, keep walking. Fortunately this road not too busy as most vehicles use a different, larger road. Sometimes there is an entrance going to the right with a security guard, just ignore it and keep walking. The security guards are here to prevent you from entering the VIP parking areas on the right, they are not here to prevent people from using the sidewalk:

Continuing on the same sidewalk, on your right you will see a motorcycles parking, then a park with a lake. Immediately after the lake, turn right (leaving Yijing Road and entering Erwei Road):

Continue on this road until the next crossroad:

On the left side of the picture above, you can see a few parked scooters, they are delivery scooters parked in front of ???. Cross the road and enter ???, it is a food court with 20 small restaurants providing all sorts of local foods (soup, noodles, dumplings, drinks, etc), at a third the price of any restaurant you can find in the airport:

If this foodcourt is not to your taste, there are a lot of other restaurants in that same street and in the backstreets of that area.

Summary

• 15 minutes walk from Terminal 3 arrivals
• GPS: 40.04501,116.59858 (OpenStreetMap-based apps such as OsmAnd work fine)

(do not mind Google Maps' wrongful paths and line names on the map above, I just use it for the satellite image)

I suspect you can't. PEK is surrounded by suburban/semi-urban areas, but the immediate surroundings of the airport terminals are runways, fields, and other large open expanses. The only ways out are the connecting roads (and subway), which do not have sidewalks.

You can try walking on the connecting roads and leave before you enter the Airport Highway, but it will be very dangerous due to these roads not having sidewalks (and only worsened by Beijing drivers' poor driving habits), and vehicles typically drive very fast. If you would rather not risk your life, I suggest saving that 10 RMB and hailing a taxi :-)

BTW, due to Chinese governmental regulations, Google Maps is very inaccurate in mainland China. You'd have to use a Chinese map application, like Baidu. But even Baidu suggests you to walk on roads without sidewalks, so I guess there's no safe way to walk out.

I don't get the notion that the lack of a sidewalk makes walking unsafe. I walked a long way out and back. Most was on sidewalk, but some was on grass where the sidewalk could have been.

Don't recall whether the flights were on time, but the scheduled times were arriving 2018 Mar 12 10:46 (Monday) and departing 2018 Mar 13 15:34 (Tuesday).

I'm having trouble finding my path on a map. I normally walk with a tracking device to record my paths, but it has an Iridium radio in it, and therefore it was in my checked luggage. I've been looking all around the airport in aerials and maps for some time and not finding anything that looks much like the very nice park I passed through. But I definitely picked the wrong road for buying food or anything else. I saw very few cars, though it was a road capable of heavy traffic. A few people walking in the park along a waterway. Almost no buildings on the way out. A few large ones on the way back. I think (not certain) that I walked outward on Sìw?i Road (???), but if that's the case, some of the buildings I see on aerials weren't there then.

I know this isn't really an answer, except as a suggestion where to not look for food.