Where to go?

On a whim, we're going to Sweden very soon for 7 days. Naturally we'll spend a good chunk of that time in Stockholm. But I'd really like to see something else, not a big city. Not necessarily a tiny town, but something that shows us another side of the country. We like museums and old stuff, quaintness, but also like to hike. And it needs to be accessible by train. Not more than 6 hours from Stockholm either please.
Any ideas?
Really appreciate your help.