My grandmother came over to America in the 1890s as a girl, my grandfather came over in 1902 as a young man. They both lived until the early 1970s (when I was in my late teens), and they both spoke with a Swedish accent, my grandfather especially so.
By 1910, Chicago had become the Swedish-American capital, with more than 100,000 immigrants making it the second largest Swedish city in the world, next to Stockholm.
That number included my granparents. There is a nice Swedish-American Museum on the north side of the city (where I grew up), devoted to the Swedish migration to Chicago.
Minnesota remains by a wide-margin the state with the most inhabitants of Swedish descent—9.6 percent of the population as of 2005.
Perhaps by percentage, Minnesota would be the largest. But in terms of absolute numbers, I would say Illinois.
“By 1910, Chicago had become the Swedish-American capital, with more than 100,000 immigrants making it the second largest Swedish city in the world, next to Stockholm.”
- From what I’ve come to understand (never having visited Chicago though), the Andersonville area of that city is known for being among the most Nordic/Swedish settlements of all places in the US. Later on, as Swedish newcomers got wealthier and got tired of local tax policies, they fled to the ‘burbs, or moved away from the Chicago area for good.
A link dealing with Chicago Swedes:
http://www.wttw.com/main.taf?p=1,7,1,1,46