Upvote:4
I think that this question will be closed as primary-opinion based, but still want to add that the best way to investigate a country is avoiding the trourist traps and select not first option you can find.
I suggest you the Eskilstuna city, there are a lot of museums there, zoo and park recreation zone you can walk in, and it is situated not very far from Stockholm: SJ (the largest train operator in Sweden) site is giving travel time near the one hour from Stockholm.
Some inspirational photos here:
Upvote:4
Yes - Eskilstuna is a nice option. The obvious ones near Stockholm (that some may consider tourist traps) are:
Other options are: