South towards Linköping, Helsingborg and Malmö
Close to trafikplats Klockaretorpet (north of the neighbourhood Klockaretorpet) along Linköpingsvägen (which is used as an on-ramp to E4) there is a passage where the road is going straight for a while, which means that hitchhikers will be visible from far. Along that straight stretch there is a bus stop where cars can stop. No matter what city you want to go it could be a good idea to write "Linköping" on the sign. If you're planning to go further south than Linköping it's a good idea to get off at the gas station and rest area Herrbeta if your driver only is going to Linköping. Herrbeta is about 20 km before Linköping and is one of the most visited rest areas along the motorway E4.
North towards Stockholm
Inbetween Ingelsta Shoppingcenter and the city center there is Stockholmsvägen. In case you get dropped at Ingelsta you can walk here (approximately 30 min). From Ingelsta just after passing the second roundabout you arrive at Stockholmsvägen, here you find a busstop where you can continue your way up north. Many cars passing here and most likely also go in the direction of Stockholm. Because of the roundabout people drive here at a normal speed, where they can read your sign properly.
This building at the beginning of Linköpingsvägen (not far from the hitchhiking spot towards the South/West) is the cafeteria of Ebersteinska gymnasiet, a local technical high school. They serve free lunch every day from 10.40 to 12.45. Just walk inside, help yourself to as many servings of salad and cooked food (usually vegetarian option, vegan is rare, but there's the salad buffet) as you like. There usually is lots of people and there is no checks as to if you're actually supposed to be there. If somebody asks you who you are, tell them you are an exchange student from Italy/Panama/Swaziland/whatever. Be discrete, don't spoil it for others, and enjoy!