Dont know a lot about Jutland. Its a place we danes prefer not to acknowledge/talk about, but Id go see Møgeltønder and Ribe coming up. First time driving into Møgeltønder felt like entering a magical kingdom to me (this was recently, so not a childhood memory).
Christiansfeld, also southern part of jutland, is on the unesco list. I dont really get it to be honest, but theres a neat graveyard.
If you pass over funen, I would recommend going to Faaborg (Fåborg). The harbour front has not been modernized, and you can find a great meal there (go deep into the harbour, avoid the booths on the front).
When youre done soaking up the old town and harbour front, hop on one of the ferries - Id go to Avernakø and rent a bike, but any of the small ferry trips will be great. You can easily spend 2-3 days island hopping. (theres a harbour festival there with old, wooden ships coming in on the 27th, which may be a little late for your schedule).
Langeland has wild horses and a great atmosphere, which will fit your budget (Free). If you engage with the locals, you can encounter some
really fun characters.
Odense, my town/centre of funen.
Checking out the newly developed area around the H.C. Andersen museum is a must. Biggest tourist attraction we have here, and highly lauded internationally right now. To a local, its just weird, but judging from the hype, it should be interesting.
There is an open air concert on Thursday evenings at Amfiscenen with a great atmosphere, where youll easily be able to talk to some locals (July 20th features a very treasured, danish "folksy" duo, as well as a more modern artist). The area there is nice, and the concert experience and arena is about as “Odense” as you can get. You can grab a beer at the student bar if you’re into younger crowd, or at the cinema cafe across from it, if you want something a little more mature.
Walk through Vintapperstræde when going there, and pass over to Brandts passage to see the nicest area of the walking streets.
In Vintapperstræde, Id recommend grabbing a piece of savory pie at “The Pie Project”, and a beer at Christian 4tal. Noodle bar “Heat” 2 minutes from Amfiscenen, also great on a budget, and close to the concert venue.
"Record Pusher" vinyl shop has a nice Friday Bar, and the area is old town.
I wrote this assuming you have a phone you can plot some of this into
