Copenhagen! Fantastic food scene - dare I say the best in Europe? Great cocktails, the boat tours are quite interesting and cute, lovely harbour area, brilliant art galleries and the amusement park is great fun. I'd easily recommend it.
Drinks: Warpigs (if you like beer, and heavy music), Jernbanecafeen is a great pub that's very unique. Full of locals, quaint and good beer selection.
Food: Kodbyens Fiskebar (modern seafood restaurant, cool setting, fantastic food and the deserts are made at your table which is fun). Flesch (it's a butcher during the day, but specializes in pork in the evening. A great restaurant. Relae - Michelin Starred, focus is on vegetables. Smart, forward thinking food.
I stayed in Absalon Hotel which is good for the fish & pork place and the two bars above. It's in a bit of gritty location, but only 5 minute walk from the amusement park and 10 from the 'centre'. Good value!
I'm actually going to Gothenburg on the 25th - 28th of Jan. There doesn't seem a huge amount to do, but should be nice to see somewhere different.