>>2561627As everyone else has said, going without transportation is bold. You can get a bus from the airport to Reykjavik (which was like 3000 kronor), but transport beyond that is virtually nil. 90% of the population speaks English, which was incredibly helpful.
Everything is expensive as hell. If you like alcohol, buy it at the airport duty free, because a pint of beer is like 1500 kronor anywhere else.
Campsites are everywhere. The cost varies wildly (1500-5000 kronor a night), but 95% of them have heated showers and public restrooms.
You are going to be wet. All. Of. The. Time. Your towels / socks will not dry out. Plan accordingly.
Gas station hot dogs are bomb (this is a thing), and look into the discount grocery store BONUS. These will be your dietary staples.
In no particular order, the following sites were pretty cool in the southern portion:
>Garður Old Lighthouse / Campground>The city of Vik, and Halldórskaffi Cafe>Black sand beach>The thousands of waterfalls on the southern end of the island, literally just pick any of them>The hundreds of hot springs, although I can't remember the name of any of them, I never went to one that sucked>Reykjavik had stuff to do all day, could spend an entire week there, check out the walk along the seaboard on the north end where the Sun Voyager, Founder statue, Harpa concert hall and Hallgrimskirkja church are. 
