Coming from the north-east, such as Stockholm, you go
south on E4. The distance from Stockholm is 330 kms. When you pass
Linköping, you have 131 kms left to go.
Coming from the west, such as Göteborg you go east
on Route 40. The distance is 149 kms. When you pass Borås, you have 83
kms left to go.
Coming from the south, such as Malmö, you go north
on E4. The distance is 293 kms, when you pass Helsingborg, you have
238 kms left to go.
Here is a link to Swebus which is a bus travel company that services
large parts of Sweden. Swebus
Trains in Sweden are run by SJ, among others. Here is a link to SJ
There is actually an airport
in Jönköping. There are daily connections Jönköping-Stockholm and Jönköping-Copenhagen
The trafic into the Gothenburg
airport is a bit more intense. Its routes
are listed here.