Behind Svartsjö Castle itself is a wonderful bit of forest. It starts off with "Kristina's" old lyme tree which is one of the oldest in Sweden and has a statue of 17th century statesman Axel Oxenstierna beneath it. Then you can wander past the castle fish ponds (housing rare lizards and frogs today) and on to wonderful oaks and grassy lakeside pastures. Just remember to close all gates if you enter fields with cows. There is also a very overgrown English garden which today looks more like a wild forest but if you ignore that it is supposed to be English, it is actually quite a fascinating place.
Walking around in the area you can also see Fiskartorpet, a listed building in the form of an old fisherman's croft. Old, solid timber without nails and a straw roof makes it very pretty.
Fondest memory: At Svartsjö, I miss the hilly oak forest (see third picture).
Favorite thing: For a great day out in rural county Stockholm, tracing the vikings, get off a bus at Adelsö Church and stroll around down to Hovgården, passed the runestone. You can then also catch a ferry to Birka (once a day in late morning summertime) or stay on Adelsö and visit the church and then the nice café with viking artefact copies for sale as well as nice pastries which can be had in the huge garden.