Been there last november, had a great time. Renting a car is almost mandatory, since there is so much distance inbetween every other point of interest (Offroad/4wd if you can, but careful, you don't want to get stuck in the middle of nowhere with no signal). Bring good trekking shoes.
If you like waterfalls, there is plenty of them Went to see Skˇgafoss and Gullfoss (also did the rest of the "golden circle", that's a good thing to start with for pictures), which was quite impressive.
The eyjafjallajokull volcano might be interesting, didn't had a chance to go there :/
Not really sure about camping though, the place is very windy since there are almost no trees (tundra style), so it highly intensifies the cold feeling. We rented a realy nice house about 2h drive from ReykjavÝk, and do not regret it one bit. We had a blast watching aurora borealis from the jaccuzzi outside
Spend a day or two in ReykjavÝk btw, it's pretty nice, and has some really good restaurants. I was quite amazed at the quantity and quality of street art there (considering the size of the city).
One thing you should definately do, is to go to the Blue Lagoon (I suspect it's much more enjoyable/fun to go there in winter, but just go there anyways !).
*edit : two restaurants in Reykjavik that I thought were really good : Sjßvargrilli (Skˇlav÷rustÝgur 14, 101 ReykjavÝk, Iceland) and Grillmarkaurinn (LŠkjargata 2A, 101 ReykjavÝk)