Yes. The western Norse ( Denmark, Norway, west coast of Sweden) went to the British Isles ( trade, tourism) , Orkneys ( settlement) , Iceland ( settlement after disagreement with one Norwegian king), Greenland ( because they were stupid
) and Northern America ( Blown off course or just to have a look)
They also went into the Med through Gibraltar.
The eastern Norse ( Sweden and Denmark) went east, founded the Rus country ( Novgorod as centre) and ventured down towards todays Turkey. Possibly/probably all around the Black Sea.
Trade, Tourism, job seeking.
The Beouwulf movies ( all) and the series Vikings depict Denmark and sounthern Norway as having serious mountains and Fjords. Wrong.
In the series Vikings ( series 1 or 2?) Old Uppsala is totally wrongly shown.
There were no Scandinavian countries in the beginning as you know, just small kingdoms/Chiefdoms. Towards the late 800' they consolidated into larger units.
That is why Iceland was populated. A guy did not wanted to be controlled by a king. Harald Harfager (Hardraga). was the king.
The thinking is that the first Norse on Iceland were groups led by a Norwegian, plus a group led by a Swede. Short stay only.
I think the concensus today is that Irish or Scottish monks lived there first. I do not think there is any supporting archeology though.