It all depends on what you want to do, hiking, canoeing, fishing, climbing, bushcrafting...
There is so many places to go to and many has their own little places were they go to. Just outside the big city of gothenburg you can find places that are totally silent and were you will not see any people.
The best place I know is Sarek if you just want to feel alone and experience beatiful nature I would recommend the fjells and especailly Sarek. It is a 2 day hike to get in to the national park or you can ride with a chopper in. But then you will miss the beauty of the untouched forest were it grows more flowers and plants then I ever seen before. When you finally get up to the fjells you will probably not see anyone until you go out again. If you are int o birdwatching you will see and hear lots of birds and will probably also see some reindeers, but if you o down to Rapadalen you can get the chance to see the giant elks, lynx, bear and many more animals that live down there.
But to hike in Sarek it take some experience in the fjells becasue you can easily get caught in a storm and get experinces that you don´t want.
But you can always live on one of the Stations and do dayhikes out onto the fjell, Saltoloukta is a really good one that serves 3 course meal every eveneing (highly recommended) and have the best sauna wiev in the world.
You can see some picture of my visit there earlier this summer
http://www.nordicbushcraft.com/privat/sarek06
But if you want to do bushcraft or survival I would recommend you to take a course in survival/bushcraft in Sweden were you will be able to cut down tree´s forage for edible plants and learn more of what you ca and can´t do in the swedihs forests.