Anyone been to either of these two places? May just have an extra day to spend and wondering which to choose after spending time in Malmo.
I've been researching Sweden for a trip originally intended to happen in 2020. I haven't been to either Vaxjo or Jonkoping yet, but my notes for Jonkoping (from various guide books, etc.) simple read, "Rather boring industrial town."
Vaxjo, while described as a quiet place, is in the area where a lot of Swedish glass is produced--a topic that interests me but probably not you. In addition to the local glass museum, which is apparently not exactly a whiz-bang experience, there's some modern glass in the cathedral. The glass-production facilities are not in Vaxjo itself and most don't appear to be easily accessible without a rental car. I believe you can get to Kosta via a combination of train and bus or two buses.
The House of Emigrants in Vaxjo might be of considerable interest if you are of Swedish ethnicity. Otherwise, it probably wouldn't be particularly exciting, especially if your family isn't close to its roots in some other country.
Vaxjo also has an attractive park near the lake and a 3-mile walking path around said lake.
Eksjo and Granna sound like they might be more engaging for folks not into Swedish glass--but this is just my impression based on pre-trip research. Granna, however, is very touristy. It gets a million visitors a year. It's known for candy-making. Eksjo seems more like the traditional tourist target--a town with colorful 17th-century buildings and cobblestone streets. The Savsjo area just to the south has a bunch of 12th-century churches.
Yes, what do you want to know? And what are you looking for? Is this a stop on the way to somewhere else or just a side trip?
Great summary by acraven and there is not much more to add. Jönköping is more than a boring industrial town though, even if large parts of the town is exactly that. There are some nice parts and the location at the southern end of lake Vättern is beautiful. For glass blowing, Växjö is a better option. The area between Växjö and Kalmar has a long history of glass making. Some glass blowers are easy to access by bus or train but for many a car will be needed.
If you are looking for small town charm, Eksjö and Gränna are much better options. While Gränna is touristy, most tourists are Scandinavian, Dutch or German. You will most likely not meet other Americans there. Central Gränna is pretty small and in a charming location overlooking Vättern. It is as mentioned famous for the candy which is still hand made there, and attracts a lot of visitors. (How it's made: https://www.youtube.com/watch?v=IjfA4j2Ibsk ) But it is also the birth place of S.A. Andrée, famous for a failed arctic expedition, and there is a museum about it in Gränna.
For a more "regular small town charm" Eksjö is a very good option.