The US dwarfs Sweden in size and cultural diversity. There are many places to live in the US that are as nice or nicer than Sweden. There are many places that are not.
There is no place in the US that beats Sweden on metrics like quality of life and healthcare affordability. These things are nationally driven, and there are no US states with socialized healthcare.
IMO most people would not consider healthcare affordability as a factor in where they want to live, or even a major factor in their quality of life. NYC (as one example) is famously expensive across the board for all types of insurance, healthcare, housing, food, etc. but still has hordes of people who want to live there.
As an aside - New York State did launch a universal healthcare program recently, and I believe Colorado has something in the works on that front too.
New York City recently launched a health insurance program that seeks to cover everyone in the city and offers low-cost options. It's not, however, a single-payer program. [0]
New York State does not have any statewide health insurance program yet, universal or otherwise. However, the New York Health Act (which would create a statewide single-payer insurance program) has passed the State Assembly four years in a row and stands a good chance of finally passing the Senate this year as well. [1]
Sweden probably has a slightly undeserved reputation in this area. These days mainly the financing is socialized, which is still something. The services themselves are privatized. So the quality can vary wildly depending on location and provider. Or even almost randomly. It is more similar to a capitalist system in that regard. I think maybe Norway or Finland might be better examples of countries offering egalitarian service today.