Denmark is expensive, make no mistake.

Some of the places in CPH that I like to frequent for drinks are The Jane, 1105, Ruby's and Zefside. The latter has okay drinks and a pretty sweet Happy Hour 2-for-1 deal.

If the weather is nice, I can highly recommend grabbing a city map and renting a bike. I did the same thing in Amsterdam and it was fantastic.

As for things to see, there are plenty of museums and beautiful buildings in the city. Really depends on what your interests are. If you're an ent, you may want to go have a look at Free City Christiania, or what is left of the trees stuff there. Clue us in on what sort of stuff you're into and we'll probably be able to aid you a tad better.

As for taboos to keep away from... Like someone else already mentioned, we are highly secularised and bringing up god/religion is going to get you ostracized quicker than you can say Jesus.

One thing to keep in mind is that Danes can seem, and in many cases are, quite reserved and stand-off'ish in the beginning, until they get some idea of what you're about.

As for showing you around, well, someone might offer, but I doubt you'll have any luck in that department unless you're ballsy enough to ask.