The hard shoulder on Malmslättsvägen just after the big roundabout "Valla Rondellen" is probably the best spot in Linköping. Easiest way to get there from centre is to take bus nr 3 towards "Ryd Centrum", get of at station "Ostbrickan", walk back a couple of hundred meters towards the McD you passed with the bus, and then climb up on to the road. If you prefer walking it is a 30 minute walk from square "Stora Torget" following "Storgatan" until it turns into "Malmslättsvägen" and then continue until you hit the roundabout, follow the bike path through it and walk up the road after the McD. The shoulder is very long and broad, even a truck can easily stop here and cars usually drive fairly slowly coming out of the roundabout. If you like some souvenirs or sight-seeing on the way you have the outdoor museum "Gamla Linköping" (old Linköping) just before the roundabout on the left side, coming from the city centre. There is a nice old-fashioned candy store and different hand crafts and the like.
You could also try the spot behind the big mall Ikano-huset next to IKEA. Take bus 10, 25 or 26 to Ikano-huset. Walk through the mall and across the big parking lot on the other side. You have to cross the slipway where the cars are going north east towards Stockholm. There is a place where cars can stop just after this slipway, and all the cars going south-west on the E4 pass here. Good place!
If you get a ride to Mjölby, which is a fair chance that you will, your best chance is probably to get off at Mantorp some 10 km down the road, where there is a gas station and restaurant on the right side. It's a tiny bit off and there is a fair amount of people there who won't go further down the highway, but it's still there and on the right side.
Northeast on the Stockholm towards
Just after Mörtlösa rondellen there is a spot on the hard shoulder shortly before the on ramp to the highway where cars have a good view and plenty of space to stop. To get there you can take bus 13 towards Tallboda and get off at station "Tallboda Centrum". From there you will walk a few hundred meters in the opposite direction of the bus on Norrköpingsvägen until roundabout "Mörtlösa Rondellen" where you will see the signs for Stockholm E4 to the right. One can also walk from the Central Station about 30-40 minutes. Nicest way is to go underneath the tracks to the oppoiste side of the station and then walk down to the river "Stångån", cross it by the bridge to your left, and walk towards the big "Saab Arena" on the opposite side of the park "Stångebrofältet". From the Arena, walk along Norrköpingsvägen, maybe 20 minutes, until you arrive at "Mörtlösa Rondellen". Many people will be going to next major city Norrköping. If so you can get off about 13 kilometres up the highway on gas station "Herrbeta". The station is pretty small, but straight on the highway, and your bound to get further from here. Depending on his mood and the hour of the day