I would go to Swedish Lapland. Kiruna is said to be one of the best places for watching the Northern lights, because they have more days with clear skies than other similar places.
However it's probably quite a touristy area (though presumably Finnish Rovaniemi is more touristy). You can get some idea of what's available by reading forum members' Radioclare and meddysong (Clare and Tim) blog -
https://timeofftakeoff.com/tags/finland In winter it's stuff like snowshoe walking, skiing, husky rides, most likely you can also visit a husky or reindeer farm. Fishing is also an option.
In summer you can of course enjoy the midnight sun, and again stuff like sports and fishing if that's your thing.
If you do go there be sure to look into ways of exploring the Saami culture.
But in your particular case, another option could be to choose a Stockholm suburb? That's where ordinary people live so you should be able to find somewhere to stay. You can certainly find some area with great nature, maybe even stay on an island if you want. Of course it would be ridiculous not to visit Stockholm a couple of times but you can plan to avoid big crowds, e.g. go on weekdays. You can also go to somewhere like Uppsala (oldest university in Sweden/Scandinavia) and probably many other places, and of course you should absolutely go to Finland as well
Speaking of Finland, if your goal is to practise your Swedish, maybe you can go to the Åland islands? That's a Swedish-speaking autonomy. There are also other places in Finland where you'll run into many Swedish speakers (Vasa, Jakobstad, Borgå - I'm listing their Swedish names here obviously), just remember that not everyone speaks/likes it
In general, have you tried this style of travelling before? If yes, where?
Perhaps consider renting a camper/trailer? I'd say if you want to avoid big cities like Stockholm, you won't see much by staying in the same place for a month. (unless you choose a specific area and explore it in detail, I guess - maybe Gotland?
a prominent forum member lives there
)
In terms of language learning, remember that Swedish has very diverse dialects (and there are some minority languages too). Not everyone is good at toning down their dialect with foreigners, to the point that switching to English may be a necessity.