Koli national park in eastern Finland is very nice. It has bit more elevation changes than most of the Finnish lakelands and quite stunning scenery.

http://www.koli.fi/en/Places-to-visit/Koli-national-park#category=sights&initialsearch=true&sorting=Name&area=null&acctype=Kansallis-+ja+luonnonpuistot

There are plenty of other national parks as well and of course plenty of nice spots that don't have any official status. I would go through this list.

http://www.nationalparks.fi/nationalparks

As mentioned in September weather is quite cool and possibly rainy. So prepare with proper gear or have a backup plan if you don't want to get wet.

I recommend to look at Lappeenranta, ca 2 hrs from Helsinki; http://www.visitlappeenranta.fi/en/

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