Hi Benjamin,
if you are visiting København of cource you will have to visit the new Bang & Olufsen store in Østergade (Strøget near Kgs. Nytorv).
Once you are there (apart from Illum as already suggested) stay away from Strøget. Walk the small sideways and the parallel-streets instead - much more interesting, in my opinion.
Take notice of the suggestions in the other posts as well!
As far as recommending places to eat, it is a bit more complicated - since I don't know how much you can spend /are willing to spend.
Noma is not the cheapest place to eat - and you would have to make a reservation long before you want to go there.
Eating/drinking is expensive in København, so - if you don't have a lot to spend (or prefer to spend it on B&O), look a bit outside the center (Østerbro/Nørrebro).
Actually there are some good places to eat in Christiania or in the nearby Christianshavn.
If you like good beer, look for some of the 'micro-breweries' http://www.nelso.dk/dk/koebenhavn/mikrobryggerier/ (you can also eat at most places).
Or visit the http://www.bishopsarms.com/K_benhavn/Presentation - lots of beer and whiskey.
If you like good coffee, it will not be hard to find places where people love coffee and know how to make good coffee:
http://www.dagh.dk/kaffe and many others.
Struer is far from København - if you want to go there plan 2 or 3 days for the trip - visiting the B&O museum there is a joy.
In Struer you can eat and drink good beer at a resonable price in "Pingvinen".
By the way, let your car rest while you are in København - use the bus/S-tog and your feet.
You can easily reach the 'Hellerup B&O-store" by bus.
And remember quite a few shops opens late and closes early - I always wonder have they manage to sell anything?
Buying B&O-stuff is not cheaper than elsewhere - unless you are able to make a good deal in one of the smaller shops.
You could look for the new headphones - please tell us afterwards if you are/were able to get them cheaper in KBH than in Belgium.
And don't forget to tell us about your journey 🙂
P.S. I often stay here: http://www.dgi-byen.com/ - if you stay at Hotel D'Angleterre you might even get a room with the newly installed BV10's 😁
Greetings Millemissen