We rented a car. The rental agency tried to charge us extra for damage from rocks hitting the bottom of the car, but ended up letting us buy the extra insurance when we dropped the car off. You need to use the pin number on your credit card to get gas.
We rented a wifi hotspot, which I would recommend. We reserved one in advance, and picked it up at a gas stiation near Reykavik.
Golden Circle towards Vik:
Thingvellir National Park (we did not but you can snorkel or scuba dive here)
Lighthouse at Dyrholaey
Reynisfara beach - black sand beach
9:30am - glacier hike and climb
Tipping after the tour was the only time we used cash.
4:10pm - Boat tour of Jokulsarlon Lagoon
Dinner at Sudar Vik
Drove to Reykavik. We were there for culture night. The city is very walkable, we never drove somewhere within the city.
Baejarins Beztu - hotdogs for lunch
Icelandic Phallological Muesum
Sandholt - sandwiches for dinner
Big Lebowski bar
Laundromat Cafe for breakfast
Reykjadalur hot springs - pretty steep hike, hot springs were great
Svarta Kaffið - great soup place, wish we could have gone again
We went to the Blue Lagoon in the morning and then to the airport to fly home in the afternoon.
We didn't do these things but they are available:
Scua or snorkel at Thingvellir National Park
Free city walking tour of Reykavik
See a show at Harpa concert hall
Ice cave tour