I'm an expat in Copenhagen and definitely find it comfortable, almost embarrassingly so. It feels like being in a foreign country on "easy" difficulty level. Not only does everyone speak English, but at least in Copenhagen, English seems to be everywhere without even asking for it explicitly. Many things from the government (websites, forms, etc.) are published bilingually in Danish/English. And it works smoothly, often over the internet; very little difficulty navigating the bureaucracy. My workplace is also probably 70% English, though I work at an IT university, so that may be non representative.
There is also a lot of "public life" that uses English as the lingua franca, so someone who doesn't speak Danish doesn't end up isolated in just a little British/American expat bubble. Any bar in the city center will have at least 15-25% of the people speaking English (partly because there are a lot of foreign students). And cultural events at museums, universities, & hackerspaces are often in English to accommodate visiting speakers, expats, foreign students, etc. Many tech events are in English because even many Danish companies have non-Danish founders or cofounders (especially true for game companies). It's interesting in part because there is so much English but the majority of people speaking it aren't native English speakers, it's just the language multinational groups end up with for practicality. That also makes Copenhagen a good place to meet many European nationalities. I've met a lot of German, Polish, and Spanish people in particular (in addition to Danish and Swedish people). Especially a lot of Germans, and except the ones who stick to all-German groups, or those who have assimilated and speak good Danish, they mostly end up in mixed groups speaking English. I think I would actually have had a hard time meeting this many Germans if I had lived in Germany; here we have some being-foreigners-in-Denmark thing in common to break the ice, and an English-speaking-by-default environment to make it easy to connect.
Of course there is a whole Danish-speaking cultural scene someone who doesn't speak Danish misses out on, and Copenhagen would be even more interesting if you speak both languages. But for a country that isn't officially English-speaking, the amount of English-language cultural stuff going on is surprisingly large.
(Oh, and the prices aren't bad. Eating out is very expensive, but rent is way cheaper than urban/walkable American cities. I moved from the SF Bay Area and rents in Copenhagen are hilariously cheap in comparison to SF. Also cheaper than NYC or Boston. Maybe roughly on par with Midtown Atlanta, to pick a point of comparison.)
There is also a lot of "public life" that uses English as the lingua franca, so someone who doesn't speak Danish doesn't end up isolated in just a little British/American expat bubble. Any bar in the city center will have at least 15-25% of the people speaking English (partly because there are a lot of foreign students). And cultural events at museums, universities, & hackerspaces are often in English to accommodate visiting speakers, expats, foreign students, etc. Many tech events are in English because even many Danish companies have non-Danish founders or cofounders (especially true for game companies). It's interesting in part because there is so much English but the majority of people speaking it aren't native English speakers, it's just the language multinational groups end up with for practicality. That also makes Copenhagen a good place to meet many European nationalities. I've met a lot of German, Polish, and Spanish people in particular (in addition to Danish and Swedish people). Especially a lot of Germans, and except the ones who stick to all-German groups, or those who have assimilated and speak good Danish, they mostly end up in mixed groups speaking English. I think I would actually have had a hard time meeting this many Germans if I had lived in Germany; here we have some being-foreigners-in-Denmark thing in common to break the ice, and an English-speaking-by-default environment to make it easy to connect.
Of course there is a whole Danish-speaking cultural scene someone who doesn't speak Danish misses out on, and Copenhagen would be even more interesting if you speak both languages. But for a country that isn't officially English-speaking, the amount of English-language cultural stuff going on is surprisingly large.
(Oh, and the prices aren't bad. Eating out is very expensive, but rent is way cheaper than urban/walkable American cities. I moved from the SF Bay Area and rents in Copenhagen are hilariously cheap in comparison to SF. Also cheaper than NYC or Boston. Maybe roughly on par with Midtown Atlanta, to pick a point of comparison.)