If you ever happen to take some days of vacation in Gilleleje – which is highly recommendable if you enjoy wind, sun and the sea – make sure you have your UMTS device with you to hook up to the internet. The only other alternative I found is a hotspot in the harbor that will sell online airtime to Danes only (as foreigner you have to visit the shop and get your voucher there. And, yes you got it right, the shop is usually closed).
Or you try your luck in Sofa.1 a café which has live Jazz on Fridays. If you ask nicely the waiters will give you the key to their wireless network.

PS: By the way: Don’t waste your time on Willy’s as listed on some other pages. They are out of business and closed there shop down.