Very few people are in Helsinki for the midsummer. Traditionally for midsummer people leave for their cottages and the Finnish cities are deserted. During midsummer you should be prepared for shorter opening hours or stores being closed.
Perhaps the most traditional midsummer celebration in Helsinki is in Seurasaari, which is an island close to the city. The website for the Midsummer celebrations is here and according to it they have a bonfire, dances and traditional performances. If you want to find a stereotypically Finnish midsummer this is probably the way to go.
Some more modern events might include music festivals such as the one in Hernesaari or Stadin Juhannus, which is also on an island near Helsinki.
Besides these, there is also a large number of smaller celebrations. Kaivopuisto and Hietaniemi are at least common places for gatherings. Unlike the others these two should be free as they are public parks, but you are not likely to find as much organized celebrations here. They should probably still have at least a bonfire and people enjoying summer at the very least.