I travelled from Linköping to Jönköping by train. It took me about 3 hours to get there, because I had two transfers (one at Tranås and then another at Nässjö), but only 2 hours to get back (only one transfer at Nässjö). The trains were efficient and on time. They were clean and tickets were checked on each one.
I really like to travel by train, I think it is a great way to see a country and I had a very nice journey to and from Jönköping.
A return second class ticket from Linköping to Jönköping will cost you about 460 SEK, but check the website below, as different fairs occur as to whether you are travelling on a regional train or the X2000 (high speed train).