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Unless there is snow (none yet) no trails there are hard. It is more about what distance you find enough. For a map, I recommend you check the trails on Openstreetmap.org. If you have android, check out this app: https://play.google.com/store/apps/details?id=se.laventura.naturkartan.tyresta
I recommend you plan it so you pass the area where the forest fire was. By bus it is not so easy to get close. Tyresta by is easiest to reach by bus, but the more interesting parts of the park are reached through other entrances.