Golden Circle
The "Golden Circle" is the area in southwest Iceland within a couple of hours' drive of Reykjavík. It has some of the area's most popular sights to see – for instance, Þingvellir, which you've already seen in the big photo at the beginning of all this.
Here's a view of the lake immediately south of Þingvellir, Þingvallavatn (which means "assembly plain water," roughly).
This is the place where Europe and America pull apart. Wahoo.
Now here's Geysir, where we get the term "geyser." The big geyser there hasn't blown in quite a while (largely because it was "encouraged" to blow a few too many times in the past), but there's a smaller one, Strokkur ("Churn"), that blows all the time. And there are hot pools and steam vents. Above: Strokkur going off, with a scenic pool in front. It's just a little roadside stop, really.
And here's the other big attraction in this direction, not too far past Geysir: Gullfoss, "golden falls." Note how the view is downward. You can't see these falls from any great distance. Actually, that's Iceland all over: you can see for miles and miles and miles, but whatever you're looking for or heading to you can't see until you're almost on top of it. No wonder the majority of Icelanders believe in the existence of "huldufolk," the "hidden people" – trolls et alia.
Here's another view of Gullfoss.
In the other direction from Reykjavík (i.e., southwest), on the Reykjanes peninsula, is Bláa Lónið, "the Blue Lagoon," which is actually outflow from a geothermal power plant. The water is plenty warm (note the steam from the outflow in the background) but runs in currents producing considerable variation within short spaces. It's full of silicates, which are supposed to be good for the skin. The pool has a soft, gravelly, sometimes squishy bottom. Note me front and centre trying to look like I'm floating. Actually, my arms are propping me up.