Þórsmörk is a photographers and hikers paradise ...and luckily I am both! Keep in mind there are many more places to stop and check out than I've listed below as always its up to you to explore what you prefer, I´m just here to help by suggesting.
Beside various guides that will help you all the way into Básar you can access Þórsmörk by a 4x4, that being said its not guaranteed you can reach all the way on your own do to the river crossings that requires an XL 4x4 - Look at the video on this page that shows most of the river crossings. From Reykjavík you'll drive the ring road or road number 1 all the way to Seljarlandsfoss
Then you get onto road Þórsmerkurveg and here is when the fun begin...depending on the road condition that is.
When me and Aron were there 15 July the road was terrible and we only had 10psi in the tyres so hopefully that tells you a bit about the road condition. On the other hand sometimes its much much better, either way just drive slow.
First stop Nauthúsagil. Have you ever walked UP a river inside a canyon, holden on to a rope across the mountain side so you dont fall into a small crator filled with water only to find a beautiful waterfall at the end.. .if not then now its time! #Nauthúsagil
Second stop Merkurker
Here you can park the car and take a look at Þórsmörk extraordinary landscape and textures. It is possible if you are equipped for it to walk up the river inside the cave as you can see on the photos here below. You can walk about and explore hidden caves that have formed, just be careful. #merkurker
Third stop Gígjökull. You will have to turn off Þórsmerkurvegi onto a road that goes towards the parking spot for looking at. I once saw a avalanche there, small one but woah the loud noises were frightening. #Gígjökull
First things first...do not cross Krossá to get over to Langidalur, you can park and walk.
Please be careful as there have been too many accidents where people misjudge the river.
With that out of the way, from these areas you can go on loads of hike and two of the most popular hiking trails end here. Hiking Laugavegur from Landmannalaugar you´ll end up in Langidalur. When you are hiking Fimmvörðuháls from Skógar you´ll end up at Básar.
Photos from Þórsmörk and Valahnúkur hike.