There are a few things on Suomenlinna: a submarine (not very expensive, might even be free for kids not sure and there is usually someone on board who just loves talking to the kids), a toy museum (not too girlie, my kids enjoyed it when they were that age) and also the underground passages (take a torch and buy the map from one of the kiosks, if it's windy take a kite).
In Espoo there is a brilliant car museum, run by a bunch of local enthusiasts. I think there is a bus going out there, I'll look for the link. edit: Not in English but this should help
http://www.saunalahti.fi/automuse/sijainti.html
Seurasaari is a nice walk and you can visit the old buildings, watch some handicrafts (sometimes) and feed the squirrels (don't forget the peanuts, but I find choc biscuits are OK too)
On a rainy day the Natural History Museum (in between Kamppi and the Railway station) is FAB (newly renovated).
You could take a bus out to Haukilahti (bus 111) or Matinkyla (132???) and spend some time just sitting on the beach, eating ice-cream, reading a book or playing beach volley. There are probably beaches east of the town centre too, but I don't know that side so well. Under 18s can fish without a permit so you could buy him a small fishing rod (eg from HongKong, Prisma etc, not very expensive) and let him try fishing.
There are island hopping ferries in Espoo that go out into the archipelago at regular intervals. Some of the islands are great for picking blueberries and generally just exploring, one or two of them have summer cafés, all are good for fishing, BBQs and picnics.
http://www.espoo.fi/default.asp?path=1; ... 6054;16056