Gullfoss is a huge waterfall, one of the most popular tourist attractions.
The original geyser. Gullfoss and Geysir are on the Golden Circle. Almost all tourists take the Golden Circle.
Þingvellir is the original seat of the Icelandic parliament, Alþingi, from 930 onwards. The last session held there in the late 18th century. The location is beautiful with a tectonic rift valley next to the biggest natural lake in Iceland, Þingvallavatn. Our parliament is still called Alþingi but as a favor to politicians they now convene in the capital. Google 'Thingvellir'.
Laugarvatn is a small town by a lake with a new thermal baths facility.
Fjara means shore, so Reynisfjara is down by the sea. Please be careful and don't get killed by the constant onslaught of massive waves. I warned you. The place is absolutely stunning and maybe your best chance to see a live puffin. For stuffed puffin of all sorts and sizes please go to downtown Reykjavík, after which they will haunt you in your strangest nightmares.
These are beautiful waterfalls
Seljavallalaug is an idyllic, old swimming pool in the middle of nowhere. Google it and be amazed. Full of tourists I'm afraid.
Flúðir is a small town only about 20 minutes drive from Skálholt. Here you can go to the not-so-secret Secret Lagoon. It's actually quite nice. It's also home to Friðheimar, a greenhouse with a nice restaurant inside. Maybe that sounds strange, but it's also nice.