"He has primarily been a freelancer, with one full-time position at an evening paper in the late eighties. He left in 1990 when he helped start the monthly magazine Millenium." - (51)
In The Girl With The Dragon Tattoo, Blomkvist helped to start and run the Swedish Magazine, Millennium, with Erika Berger, staying on its board at the beginning as its co-owner and publisher. Millennium is a left-winged financial magazine that writes about companies of large and small sizes, and is most known for uncovering conspiracies and criticizing actions of businesses.

However, the inspiration for this comes from the magazine that Larson helped to start up and was the editor-in-cheif for in 1995, which went by the name Expo. It was not connected to any one group, politically or financially, however was seen as being left-leaning due to its investigative journalism focused on studying and mapping nationalism, racist, anti-democratic, anti-semite, and far-right movements and organizations. This sounds a lot like how the Millennium operated in many respects.
In fact, Larson mentions several real-life Swedish magazines and publications in The Girl With The Dragon Tattoo. Included, but not limited are:

Arena - A left-leaning, bi-monthly magazine. It publishes reports, interviews and essays on politics and culture. (Mentioned at page 51)

Aftonbladet - A tabloid that has changed its leanings over a number a years, first starting out as an " independent social-democratic" paper, that later went from leaning over as a liberal to a conservative over the year. (Mentioned on page 270)

Metro - A freesheet (free distribution) paper meant for commuters and those on the run. The distributing company has grown large enough on an international scale, such that it has publications for North America, parts of South America, Europe, and parts of Asia. (Mentioned on pg 270)

Ordfront - A left-orientated magazine by a publish house of the same name. It publishes about social and cultural life of Sweden and has been publishing strong for 40 years now. (Mentioned on pg 51)

Dagens Nyheter - Translates to "Todays News", its one of Sweden's largest and prominent morning papers. (Mentioned on pg 269)