There's usually one in Suomenlinna, too - and it's for FREE. And probably not as crowded as Seurasaari might be...
I was there a few years ago. I'm not sure if it's always in the same place, but then it was found like this: when you step off the ferry (near where there's a small bell tower with a clock), you immediately head right and cross the bridge. Then, after the bridge, turn left and keep on walking until you cross another bridge... after which you turn right and follow the road until after perhaps 200 metres you come to a small beach - where this bonfire was back then.
(I haven't been to Seurasaari midsummer, but there weren't any drunken idiots at the Suomenlinna bonfire either -myself perhaps excepted- it was a bit difficult to find, perhaps that kept the "four wheel drives" at bay

)
In this
map... it's in Länsi-Mustasaari, upper left corner, near the black thingy. But once again, I'm not 100% sure if it's that particular place each year. The Suomenlinna info might know...
http://www.suomenlinna.fi
The scenery is nice, especially if we're blessed with proper weather...
And there are some cool cannons nearby
Plus of course that weather permitting there's no place for a picnic in Helsinki like Suomenlinna!
(You need to pay the ticket for the ferry of course, but it's in HKL zone so if you have a monthly ticket you can just use that... and it's only a few Euros anyway)