If you only have one day in Iceland, the Golden Circle is what you're supposed to do.
(Yes, I did things backwards, but the riding tour we wanted was only available on the Monday and I wanted to do the whale watching early so we could reschedule in the event of a weather cancellation).
Ideally, you should do this on the first day of your trip. And with a small operator. There are operators that take 60 person buses...and then there are ones that take 12 person minibuses. Guess which is better? Now, we did have one person on our tour who apparently believed anything anyone told her and asked some interesting questions, among them "Is it true that the ancient vikings didn't eat fish?"
That aside, despite a miserable day, we did enjoy the tour. The Golden Circle consists of three destinations. All of them are, to some degree, tourist traps - but sometimes tourist traps can be fun.
Stop 1: The Golden Falls
The Golden Falls are the largest waterfall in Iceland and one of the most spectacular in the world. They aren't that high, but they're wide and run at an odd angle through the gorge.
You can see why rain jackets are recommended for this trip even if it's a nice day...look at that spray! Oh, and if possible, eat at the cafe here. Get the traditional Icelandic lamb stew, which is absolutely delicious and rich with bone marrow and rutabagas.
Stop 2: Geysir
The original geysir after which all the others are named is all but dormant now. It does go off every few weeks, but you have to be insanely lucky. Fortunately, a nearby one, Strokkur, is still reliable - every two minutes or so.
The site also has multi-colored hot springs. In all kinds of hues. Don't cross the fences - they're scalding hot. And be aware that if it's a wet day, the soil around here is clay. I still haven't quite got the shoes I was wearing clean.
Stop 3: Thingvellir
Here's an interesting thing about Iceland: It's the only European country never to have had its own king. (External conquerors who never lived there don't count). Instead, Iceland was governed by the Althingr - Europe's first parliament. (The Isle of Man argues that theirs is older, but the linguistic proof is that the Tynwald was named after Thingvellir - however, they do win the prize for the longest-running, as the Tynwald still meets at the same site, albeit no longer outside).
The Althingr met at Thingvellir because it was at the point where all the pack roads crossing Iceland met - the ultimate crossroads. Or, as I put it, "equally inconvenient for everyone." Nowadays the Althingr meets in Reykjavik, but occasionally ceremonies are held at Thingvellir and the President's Summer House is used for diplomatic functions. It's Iceland's original capital...
...and yeah. That's the President's Summer House. That and the church? The only things here. (There's also a visitor's center). Thingvellir is also a rift valley, falling where the Mid-Atlantic ridge passes through the island. There's even a point here that's the, shall we say "official" meeting of the two continental plates with a sign to be photographed by. If you go for that sort of thing. It's an arbitrary point, anyway - the entire valley is where the plates meet and grind against each other.
As you can see, it really was a horrible day weather-wise. Ah well.