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This was basically below where I stayed last time, really nice. There's a little place called Kalaset just over the road which is nice also. Ate at Brod&Ol which was great, Refused to go in WarPigs as they were blasting the Fratelli's.
Kompute-
My boyfriend @IdealStandard moved here to study two years ago (he works at Kalaset! Used to work at WarPigs - might have been the Fratelli's that put him off), and I came out to join him a year ago. I don't speak Danish, but I've got a job as a copywriter at an agency that works mainly in English. Before this job, I was working as a trainee mechanic in a bike shop, and also at a cafe where I spoke English, and started picking up a bit of Danish.
Not sure what kind of work you're looking for, but service/retail jobs are pretty easy to come by as a non-Danish speaker – handing out CVs/getting an intro is pretty much the only way to get in. If you're looking for something else, most companies use LinkedIn. But then there are a few specific sites for things, like architecture-specific listing etc... There are a few sites for start up and UX stuff too.. I think http://danskdynamit.com/ had a few bits too...
On a side note, I find that people are v open to random networking here.. I had a few random coffee meetings with people who worked for orgs that I wanted to squeeze my way into, and they'd always give a good hour of their time. It lead to a bit of freelance work when I first got here, until I found my current job on LinkedIn...
Anyway, hope this helps. Good luck!
speculoos
Mikropolis might be worth a visit as well: https://www.facebook.com/MikropolisBar/