Blue lagoon hot springs, about an hour's drive from Reikjavik.
 

There is a place in the south near Vik [sic] called Dyrholeay. That would be my first choice.

Also worth visiting is Dettifoss, in the Icelandic desert. This is fun for nav types as it is quite difficult to navigate to despite the claim that it is the biggest waterfall in Europe (of course, the roads, maps, and signage are probably much better now, I was there 20 years ago). There was a cairn there, I think for people to put a rock on just for finding the thing.

If you just simply drive a loop around the ring road (something I totally recommend doing), you will see tons of waterfalls just falling off the country. My favorite of these is seljalandfoss; I think it is somewhere between Keflavik and Vik on the south, tho my memory escapes me at the moment.

If you go to Akuyeri (on the north coast) there is a volcano you can hike up. I forget the name, and I believe it is extinct.

-- Randy