No problem at both places. I have never been outside of the terminal area at Shanghai Pudong, so I can't give you any pointers.
Both airports have excellent non-official areas. There are lots of guard patrols but they will leave you alone. Some even looked through my binoculars.
Shanghai Hongqiao (older, domestic only airport): I have only gone during the winter and always operations were to the south. At that end, you can shoot aircraft on arrivals and departures by positioning yourself around the area. It takes about 30/40 minutes walk from the terminal.
Beijing: To the west of the CZ
terminal, a road will go under the taxiways linking the east-side and west-side runways. A good place is just before the road goes under the taxiways and the other on the otherside. There's probably other places but this would require some form of transport other than by foot.
Also, if you are spending one week at Beijing, check out the Air Force Museum at Datanshang about 1 hour north of Beijing. Ask your hotel for a car hire, cost ends up being about $100 a day.