European route E4 goes directly to Jönköping from Helsingborg and Stockholm and offers good driving conditions and is almost a continuous motorway all the way. You can travel directly on E4 from Stockholm Arlanda Airport to DreamHack in about four hours.
Approximate travel times
Göteborg to Jönköping: 1h 50 min
Stockholm to Jönköping: 3h 30 min
Malmö to Jönköping: 3h 20 min
There are 6500 parking spaces directly outside Elmia, please see the Elmia website here for more details on prices and payment methods.