Žingvellir National Park is the easiest place to get to if you want to stand on both the Eurasian and North American teutonic plates. It's a part of the Golden Circle route that includes Gulfoss and Geysir. You can easily do this all in one day, but two might be better.
Žingvellir:
Gulfoss:
Geysir:
Oh, and be aware, their horses are kinda small. A guy my size can almost overwhelm them. Their weird little "tolt" gait is surprisingly smooth and comfortable.
And finally, beware the rental car companies. Their favorite trick is to charge customer after customer for the same damage that they never fix. Do the pre-departure inspection and take pictures, with the agent in tow. They used to like to nail us when they saw we were actually there on business and probably didn't care if our company got charged. By the time I returned with my wife (twice, I like it there that much), I had learned this game. They tried anyway.
The northern lights tours are a bit of a sham. You can spend all night chasing them (don't even try in June). The colors are seldom as spectacular as we see in the photos - those colors are enhanced by the filters on their lenses, and post-production work. They are still cool, just not what you might expect.
If you get a chance to catch a ride on one of their big glacier tour rigs, you might like that as well. They can take you way, way out there into some serious snow country. Absolutely beautiful.
All in all, one of my favorite places to go. Kinda spendy, but worth it.