Outside Linköping is Göta Kanal, (which is most famous for being the place where a popular swedish movie was made :)
It's very beautiful in summer (this photo is taken in spring, so it is not as green as it usually is) and a great place to go swimming.
Pressbyråns are the Swedish equivalent of a 7/11. You can get confectionary (lollies and chocolate), chips, drinks, newspapers, magazines, stamps and (small) post packages and even in some (that have the ATG sign) place bets.
Their prices are a little higher than what you find things for in a supermarket (e.g. 50cl bottle of Coca-Cola is 19 SEK, in a supermarket like Hemköp that would cost 10,90 SEK), but the Pressbyråns are very convenient to use.
In Linköping there is one at the central station (you can also buy a bus pass there as well), at Stora Torget and one on Fogdegatan in Skäggetorp (north-west of the city).
Favorite thing: Take the time to see the nature and get to know the people. Trädgårdsförenigen is a great park in the middle of the city. In the spring and in the summer all the flowers are blooming and it is the place everyone goes to soak up the sun during their lunch breaks and time off.