Skogafoss is a two hour drive from Reykjavik. Follow the Ring Road eastwards from Reykjavik, and you will be able see the waterfalls from the road

Thorsmork Valley
You should drive there by yourself. Note, that only 4×4 vehicles are allowed to make the journey! The other option
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Directly from the waterfall, you can start the Fimmvorduhals hike from Skogar to Thorsmork. It’s about 25km with 1000m of elevation. This was one of the greatest hike of my life, definetly worth it. The tricky part is the bus to come back to your car : Thorsmok valley is unaccessible by car so you need a special ride (about 60$) to come back to the nearest city. The rest has to be done hitchhiking.