New York, Los Angeles, San Francisco, Boston, Washington, Miami or (ideally) Hawaii. Ah, ok, all of those places are heavily urbanized and politically will not be all to different from Sweden. Let me run down my personal opinions on some of them.
New York: New York isn't quite enough of a description, foreigners often imagine New York as being one large uniform area but it is very different from that. New York has many different neighborhoods, there is Brookly, Queens, Manhattan, Harlem, the Bronx, etc. etc. All of those are very dense cities but each is different as well. New York is a tough place to live though, a lot of New Yorkers who have families actually live in Connecticut suburbs and commute to New York, but that tends to be rather expensive.
Los Angeles: I live in LA so I know the best about this one. LA isn't a city like New York is, LA is more like a massive suburb, it takes hours to drive from one end to the other, and there isn't really an "end," it just merges into other counties and districts. The best places to live are on the west side of LA: Santa Monica, Pacific Palisades, Beverly Hills, Westwood, West Hollywood, Culver city. Those are the places you see in movies. The east side of LA isn't quite as nice, those areas tend to be made up largely of immigrant populations these days actually, but if you can secure a nice salary west LA is a nice place to live, you will learn to miss snow though. LA and SF also have a culture that is more like Sweden's than the other cities you mentioned, people are laid back and unpretentious, nobody thinks they are better than anybody else on the west coast. You will probably want to send your kids to private school if you live here though, with some notable exceptions LA schools are not very good.
San Francisco: SF is great these days if you can afford it, beautiful city, good culture and people, lots of stuff in the ITT sector, it makes a lot of since, commuting is pretty awful if you live in the city though.
Boston: I have limited experience with Boston but from what I gathered it seems like a nice town, there is a more obvious class divide though between the wealthy and the poor there. I also find it to have a touch of elitism and "old money" attitude, which might be hard to deal with for someone coming from Sweden.
Washington & Miami: I don't know, sorry
Hawaii: A lot of people say they want to live in Hawaii, it seems like a great place, but it is really inconvenient to live there. Not a lot of jobs and it is difficult to get around. There really just isn't much there. Most people who move there end up leaving, it looks beautiful but it is not an easy place to live.